Surface Area of Prisms and Cylinders practice problems

well hell and welcome youtube mr robinson back here with another brand new exciting video all math based of course as always it is an honor and privilege to be serving you here today as it is every day here in my virtual classroom if you step on inside guys we are looking back in the integrated math three realm on solids and last time we were in the last module in the last review of everything we did we were looking at the volume of solids filling it up with water sand what have you with cubic units well that is you know what if you want to put something inside it and fill it up and what space could it occupy now we're going to talk about what's called the surface area and if you imagine guys 3d shapes and figures like this water bottle that have right here and stuff it's not what can fill in that we're going to answer it's how you can cover the outside if you wanted to paint it if you wanted to wrap it around with something christmas wrapping paper you know something like that just how much would it cover what is its area and it's really weird to talk about area with three-dimensional figure and that's exactly what we're going to be doing in such way that we're going to be representing these two-dimensionally that sounds weird right we're going to take what appears like box i'm looking at the first problem now we're going to take what appears like box and we're going to unfold the faces of the box and lay it out flat so we can understand what it means to collect the area the surface area of these shapes how much it would take to cover the outside and it takes little bit to kind of digest really do recommend that you do draw these surface areas to excuse me these what are called net drawings to help you with it i'm going to recommend it to my students or i'll be drawing it out every time to kind of just preach what practice and from there think the formulas are going to make sense so if you'll indulge me guys as do these problems slowly to begin with you'll start to understand what mean by these formulas as we go into them and just please follow along with the terms that i'm going to use on each of them and after that hopefully we can kick it into high year and go lot faster because this time it's going to be based on prisms and cylinders eventually we're going to get into pyramids and cones and even think even spheres with them and if we do well it's just going to be little different think these are the easiest of them and you know we're just going to play with it little bit just go with me here all right so i'm going to do forget it was eight or ten have the possibility of doing ten practice problems think i'm just gonna do eight of them your time and everything else and you know eventually they run their course little bit but here we go find the lateral area and surface area of each prism honestly i'm focused on the surface area lateral area will come with it there are bunch of areas that do want to find out and you know lateral is going to be one of them so surface area in general what is it going to mean it means that got to find the area of this face right here and this face right here and this face right here and the one that's underneath and the ones on this left side and the one that's on the back got to find the area of every single face right there add them all together and that will give you the surface area if you can see around the box that is the surface of the box now they talk about lateral area here as well and there's another thing that we could be talking about which is base areas or bases area because there are things called lateral faces and things called base faces for each prism that we're referring to so here's what's going to happen and this can be little tough for you to digest because don't really have one to kind of show you right now you can do this with cereal box with your package of something that you have but i'm going to unfold this box okay i'm going to unfold this box and i'm going to kind of give them some numbers to help you here all right let's call this front face right here number one face one and this one on the right let's call it face two over here on the left side let's call it face three i'm gonna call it in such way don't know if this is gonna make sense but it's gonna be written backwards it's like if you're looking through on the other side of the bucket i'm not going to do that that's weird face three how about face four in the back sounds good and then five on the top five is on the top and six is on the bottom okay one in the front this is tough right what i'm going to do is i'm going to unfold this box i'm going to take the top and i'm going to unfold it upward and i'm going to take the bottom i'm going to unfold it downward outward in such way so that check this out if one was right here facing us let's fold five upward so it comes up like this because we're going to flatten out this entire thing five is unfolding upward six is unfolding downward underneath it hope you're with me so far this is really tough unless you take box with yourself and make sense of this unfolding of these things as they come upward and outward now i'm going to take two the one that's on the right side of one and i'm going to fold this one outward it is on the right side it's going to stay on the right side and 3 i'm going to fold out from the left side over here and you know we want one of these we want 4 to be attached either to 2 or to 3. i'll have it attached to 3 just so it sequentially makes little sense right there 4. this is what is called guys net drawing net drawing okay net drawing is the unfolding and flattening into two-dimensional representation of your surfaces of your figure of your solid in this case prism and prisms will have this kind of representation of rectangular lateral faces remember these ones one two three and four these are called the lateral faces right here and then five and six is they were on top and bottom and i'm saying that in such way that represented them as bases being on top and bottom this is bass face bass place and this is bass face right here now we're definitely not done with everything the net drawing is just giving the representation of what it is that we need to begin with all right it still gets little confusing with here still even given you formula look you can find the area of each individual one and then add them up that's fine but there's kind of nice slicker way of doing it you know based on what there is and hope that this breakdown is going to totally make sense with it or you've probably heard it before and you're like just get on with the problem well this is my way of getting it to understand every single time after so can go faster once see another prism of the same ilk all right it's just actually what kind of shapes are we gonna have here all right think i'm gonna skip number four well don't know might do number four if you know how to find areas of hexagons i'll do number four with you that's fine all right so let's keep going with this so what you have here guys you also do have these representations if you look at face one there's length of five right here five feet and then its height is three feet right here now because these are rectangles that means all these will be three this will be three feet this will be three feet right there's height of three everywhere so i'm just gonna put three so that's three can't do it can't not put the feet so that's three feet right there three feet on that side this is basically guys large rectangle right here of all your prisms when you unfold the lateral faces you will get representation of long rectangle how long is the rectangle well we know it's as tall as the prism's height right three feet but how long does this get here well consider all the different lengths that we're looking at here we got five feet going across face one then we got seven feet going across face two that's kind of neat so can say seven feet right there once again you know that that's three now faces three and four look this is rectangular prism and something we know about rectangles is opposite sides are congruent if this is five so is this that means that four has five foot width bottom and then three has seven foot one because that's across from face two there so that's seven foot width bottom and you know total we could add all these things up and that would get the entire length right here and will i'm going to add all this those things up but it's not just writing this out to add these things up that you need to do that's not necessity all depending on what you know about the shape what you can do is look at this shape and understand what happens when add 5 with 7 with 5 with 7 not just the numbers not just the answer what is that representation look at this right here one two three four first of all this is making the rectangular base this number six right here this this is the outline of the base am adding up all the sides of the base you know what that's called that's called the perimeter when add the fives and the sevens all together i'm getting the equivalent this thing right here this unfolding that is the perimeter of your base because see how this five lines up with the 6 right there the 7 is supposed to line up with that the 5 here is supposed to line up with that instead this is the perimeter of your base this length in your lateral faces all unfolded is the perimeter of your base and this is all going to be important when i'm going to write out my formula and then this is of course the height of your prism so that's cool that is awesome we're going to find those things out so let's start writing out formula based on all the stuff i'm breaking down on problem number one know i'm going almost 10 minutes to problem number one but promise this is all gonna help you here so surface area of prism comes in the form of doing the two following things you gotta find the lateral area the area of the entire unfolding of all your lateral faces you got to find the lateral area that's what they want us to do and you got to find the area of both of your bases too right you're going to add up everything the good news is the area of one base is congruent to the area of the other base that's how prisms work and we've used capital as the area of one if you double it up that's what you get so this is how you find the surface area of prism surface area of prism is the lateral area plus the area of your two bases how do you find the lateral area all on its own well as we noticed it's large rectangle so it should be length times width but what is that length in that width the length is the perimeter of your base it's the perimeter of your base and the width if you will is the height of the prism perimeter of base times height so it takes little to cover to uncover everything that we're doing there it's little bit but we'll deal with it and once you kind of have the formulas you just kind of plug things in and you're good to go now how do you find the area of the bases it depends on the nature of the base these bases are rectangles so i'm going to do length times width and make sure that you do recognize that you know there's one part haven't written out here that that would be seven footer right there five by seven like that so here we go let's find these things let's start with the area of base that should be pretty easy the area of single base would be as said 5 times 7 and that's going to be 35 square feet cool that means that the area of two bases would you know you double that the lateral area is going to be the perimeter of the base times the height so we got to do five plus seven plus five plus seven that's the perimeter base times the prism's height which is three so that's what we're doing perimeter of base times height that's going to be times 3 which is 72 72 square feet so we have the perimeter excuse me we have the area of base we have the lateral area let's find the entire and they they're asking us to find the lateral area okay found it i'm going to do that each time the surface area is the lateral area i'm going to write this one more time lateral area plus the area of both bases so that's going to be the 72 plus 2 72 plus 70 gives us square feet now this is area this is not volume so it is square feet not cubic feet you can tell square feet square feet we're added there we found the surface area of the entire thing this is how much square footage would be needed to do whatever is you wanted to with it including just calculate it and the net drawing does assist you little bit in what goes where and what you're trying to look for and really helped explain the formula that's really why wanted to make the drawing in the first place maybe at some point you can understand how to do one without net drawing but as long as get unique shape want to give that drawing at least to begin with so triangular prism comes next we'll do that now another kind of good news thing about this guys is that you know right now i'm talking about surface area but did come from volume before it's not out of the question for some test or do something ask or whatever at some point to ask you to not only just find the surface area of your solid but also the volume of your solid at the same time and part of the good news is although it's not really this wholesome you know thing sometimes the information you're trying to find in one helps you find information for the other know we've never had to do lateral area and perimeter base but we have had to do we have had to do area of base before and when we get to some of the cylinders we're gonna have to sometimes find the radius and find the area of circle and stuff so you're on your way to getting your answer to something within volume by using information here that we would need right what is the volume of this thing it's going to be area of base times height so it's gonna be 35 times three got it it's 105 cubic feet already got the answer so it's kind of nice that you can almost kill two birds with one stone just by pulling out the information and organizing it in such way that is helpful to you all right about 14 minutes on one problem here it's not guaranteed we'll go super fast in all the rest of them but now you know what it is we're trying to do lateral area plus area of both bases lateral area is perimeter base times height but still want to focus on the net drawings and making sure you get what's happening there sorry hate when my thing does that all right number two whoa can't explain why it does that have no idea number two we have this triangular prism right here now remember the triangles are the bases those are the top and bottom that we're going to unfold from the top and bottom they're not always drawn on the top and bottom the rectangles are the lateral faces right those are the lateral faces so this time i'm going to use my rectangle tool i'm just going to draw this larger rectangle as it is the unfolding of those rectangles how many rectangles are there because of the triangle the nature of the triangle having three sides each edge gives you respective face so they're gonna be three faces to this triangle and i'm not drawing this to scale i'm just giving you three faces here three faces right here let's call this front one i'm not going to call it one and stuff but let's let's say that this front one represents this one right here so have five centimeter width of that front face with of course height of two centimeters all around let me just put it right there and then this one on the right that unfolds outward is three centimeters in width like that or in length and then this one that folds out this way has four centimeters like that see if that makes sense just this is just the rectangles the wreck the three rectangles unfolded are right there now on top have this triangle right here let's say that you know as this this part represents right there if you know what mean i'm going to unfold this flap up and outward in such way that now have triangle that's doing you know this let me give the line tool triangle that's doing this right there unfolded it upward so you have the equivalent of well this was you know this is five centimeters here this is four centimeters this is three centimeters like that all right so there's that triangle and then have the downward triangle that's you know underneath right there so have once again you know four and three four centimeters three centimeters you know like that so there is your whoa there's your triangular unfolded into its net drawing equivalent okay that's what you have now there's information that this thing doesn't contain and as i'm looking at it i'm questioning what they expect you to know and what they expect you not to know and got to tell you one of these things right now guys this triangle these triangles right here this 3 4 5 that is actually right triangle they didn't tell you it don't know if you know anything about pythagorean triples but squared plus squared equals squared means 9 plus 16 equals 25 means that this thing actually is right triangle and that's important because how else could find this area need one half base times height of triangle so need to know what are two perpendicular parts three and four are perpendicular to each other that was actually requirement of mine to know right they didn't really tell me that so let's go ahead and work that one out here let's want to use black let's use purple so the area of the base once again it's one half base times height because it is triangle and need to identify base and height is you know three and four so because they meet perpendicularly that's kind of the idea half of four is two two times three is six so got six square centimeters for single base the lateral area is once again going to be perimeter of base times height it's this entire rectangle here four plus five plus three represents this entire width right here perimeter of base times the height of the prism is 2 4 plus 5 is 9 plus 3 is 12 12 times 2 is 24 that's 24 square centimeters for the lateral area so this so that is they asked us for it so there it is the surface area is going to be the lateral area plus two base areas because there are two congruent triangles both the same ilk so that's 24 let's just do this in one 24 plus 12 is 36 36 square centimeter surface area of that triangular prism and one more time excuse me if wanted to find i'll write out the volume this time guys it's really fast the volume of this thing is area of base times height have the area of the base found it already it's six know the height it's two that is going to be 12 cubic centimeters right there they didn't ask for it i'm just letting you know that you are on your way to finding one if you found information if you use the information to find the other we didn't use lateral area for volume but we used the area of the base and that you know took moment to figure out with that right angle stuff so kind of nice that you can kind of do two and one and really it's something worth practicing because you just came off of that and you can bet you're going to be using it again all right number three this time i'm not going to do the net drawing want to see if we can understand what it is that we have without it will do net drawing number four because it's kind of out there but number three once again it's rectangle well it's square prism have square base on bottom and top and then have these rectangles that would unfold so how would these rectangles unfold though remember this goes five all the way around this is five that's five this is five that's five our surface area is lateral area plus area of both bases all right the area of your base as it's square let's square the 5 and we get 25 square centimeters that's good lateral area once again guys it's perimeter of base times height of prism the base perimeter is all four of these fives here so five times four is the perimeter of five plus five plus five plus five perimeter of your base and then times the height of the prism the height is 10 that's going to give you the lateral area that's 20 times 10 which is 200 square centimeters probably should have written five plus five plus five plus five but was just giving you kind of the faster version of that all right that's the lateral area your surface area is that lateral area plus your two bases one on top one on bottom and you get 200 plus two times 25 2 times 25 is 50 200 plus 50 is 250 square centimeters don't get me started on how fast volume would be to find actually volume is also it's 250 cubic centimeters that's interesting same volume not not really same number representing volume as it does surface area cool all right number four was thinking about not doing this one only because i'm not talking about to my students about it but if you guys are doing some on your own with these great let me show you little bit about it want to go fast and give you the net drawing and then give you the area of any sort of regular polygon here all right first of all you know we have six sided shape on top and bottom that means there are six rectangles wrapped around so when you unfold this thing right there are the your lateral faces represent six six different rectangles here and they actually are congruent don't know if i'm gonna be able to draw them perfectly congruent i'm not really attempting to just want to have six of them but they do mark up the fact that right here you see them on top all these are congruent that's kind of important don't think could have gotten the area without that information but this is regular hexagon on top and bottom all 12 meters each 12 12 meters in width here 12 12 12 12 12. so 12 meters across me do single tick marks like that to get that representation going the height of the prism is 15 meters here and then you have regular hexagons on top and bottom now got tool that can do that for me right here great kind of overlap with the shape there you know they unfold on top and bottom hope you're kind of getting the gist of the unfolding practice that's going on here yeah that's that's kind of what's kind of what's happening and then they give you this 10.39 now this if you're one of my students you're not viewing this problem anyways you're not paying attention right here this thing is called an apothem apothem is the shortest distance from center of your regular polygon to any one side which means it makes right angle going in that direction think they made right angle symbol there that is 10.39 meters i'm sure they might be asking you to find this area in different ways maybe they want you to find the area of small triangle bet that's probably what they're trying to do otherwise they won't mark these things here congruent but let me give you how the area of regular polygon works on top of the eggs you could find the area of this triangle and multiply by how many triangles there are 12 of them but here's how you'll find the area of regular polygon it's one half apothem times perimeter you just found out how perimeter works and guess what we get to find we we get to use perimeter more than once here we get to use it for lateral area as well so let's find out the perimeter of this base perimeter of the base is meters each times six sides 12 times 6 is 72 meters the apothem is 10.39 meters don't have my calculator out so that's kind of so the base area is going to be one-half 10.39 which of course is approximated times 72 know half of 72 is 36 so got to do 36 times 10.39 here we go 36 times 10.39 i'm getting 374.04 do not round this number if they didn't tell us to 300 did divide yeah did took half of it 374.04 square centimeters that is the area of single base let me double that to be safe and know what that that is when it's doubled times two 748.08 i'll have that one on the side for myself all right lateral area we still need the perimeter of base times height we know the perimeter of the base right it's 72. we already got that information like said like when you can use more than one thing and you have it organized so you know where it is lateral area is going to be perimeter of base times height like that 72 748.08 i'm gonna remember that 72 times 15. 1080 1080. feel like should have known that lateral area is 1080 square meters all right here we go let's find that surface area now surface area is your lateral area plus two base areas which is going to be 1080 plus 748.08 1080 plus 748.08 is 1828.08 square not centimeters square meters that would be wrong square meters that is your surface area of your hexagonal prism all right hexagonal prism yeah there are kind of different ways you can work that out once again if you found the area of single triangle you found out this was six meters here one half base times height multiply by 12. you can figure it out bunch of different ways there kind of give you the shorthand version something hope to run into in other videos do but not doing with my students yet don't think they learned it last year so not bothering with that all right so that's the first page there that's the first four problems let's see if we dive in some cylinders now we do and this and some composite figures great so seven and eight i'll end on seven and eight know there's nine and ten of composite i'm gonna leave them time will work against me here as i'm already 25 minutes in let's play now numbers five and six guys we're these are cylinders now they're no longer prisms but what is cylinder but circular prism i've said that before so the volume of prism if you think it's any not the volume the surface area surface area of prism if you think it's any different from the surface area of cylinder you'd be wrong it is the lateral area plus the area of the two bases and the lateral area is no different it's still perimeter of base times height but because we're dealing with circles there are ways that you can write this stuff out that's kind of nicer like as in it's only specific to this see in the last one we had rectangular prism square prism triangular prism and hexagonal prism and perimeter was added mean you added it up but the area the base was always different it was either base times height or side squared or one half aperture times perimeter one half based on site just they always change circles are always having an area of base my thing kind of crashed here hold on second there we go circles always have an area of base that's pi squared and we'll talk about the lateral area as well because there's specific way we can write that so as everything appears circular too do want you to know that if you unfold the lateral facing right here and it kind of is single facing this time it is still rectangle think of soup can with label on it if you take think of my water bottle right here with this label on it if take this label off don't know where the label thing is hold please math teachers know how to take off label here yeah the water bottle's circular but if take this label off can't really there we go if take this label off this label guys is rectangle this label unfolded is rectangle okay now think it's important for me to show here how long is we know how tall it is it's it's as tall as you saw it when it was on the thing but how long is it well if it goes around the reach of your object if it goes around the reach of your object if our object's circle that reach around we don't call perimeter for circle we call it circumference so this length right here that goes across the top or the bottom we don't need to call perimeter because that's not circle we call it the circumference it's the circumference of your base of your circle on top and bottom that's what it is so when we're doing this right here let's start with the unfolding remember it is rectangle that's unfolded right here so like that just you know nice and long we do have circles on top and bottom know this is kind of weird to kind of perceive as an unfolding here but got circle on top just copy and paste that same size and all the circle on bottom and that is your net drawing everything again two bases and lateral area that's once again rectangle so none of that changed we know that the radius of this circle here is 3 feet we know that the height of the prism is 4 feet what we need to find is of course base area with pi squared and then we need to find out what this length is right here now just mentioned it is your circumference of your circle this length right here this length is the same as this length this thing taken and unfolded unfolded represents this whole thing right here circumference of circle is 2 pi so the reason wanted to mention mention this whole thing right here is when you find the lateral area of cylinders you are going to be doing perimeter of base which is circumference perimeter of base times height perimeter bit circumference times height circumference of circles 2 pi pi times the height of your prism so if you want to write the surface area put prism here did mean to write cylinder i'm sorry even though listen they're the same thing right cylinder is the same thing but if you want specific version of it if you want it specifically and this one's kind of cool to write because it if you had to like memorize it it's check this out it's going to be lateral area which is two pi plus two bases 2 pi squareds 2 pi plus 2 pi squared i'll go ahead and use that one as long as we're talking about cylinders it is the area of both your bases and then the perimeter base temp site but it's just kind of nicer way to put that in if you have access to it you can go and use that so let's come up with the circumference of this thing let's let's do it all actually you know what you just want to plug it in just said would let's do that let's plug it all in the surface area they do say find the lateral area but you know what it's all going to be within here surface area is 2 pi plus 2 pi squared think next time i'm going to do the other kind of mundane version area based lateral area add them together because in case you ever have to find the volume with it don't want you to you know lose your lose your work 2 times 3 leave your answer in terms of pi 2 times 3 is 6 times 4 is 24 so get 24 pi here plus 3 squared is 9 times 2 is 18 get 18 pi here so surface area is going to be 42 pi square feet there it is this is the lateral area this was the area of both of your bases of both of them right there all right cool that's number five let's look at number six now which is even though the cylinder the circles here are on the side with the cylinder these are still your bases if drew net and unfolded it that's that's what we'd be dealing with by the way this circumference 2 pi 2 times pi times radius 3. this would have been 6 pi right there that would have been 6 pi feet okay so i'm not going to do net drawing this time let's let's actually do area of base and let's do lateral area and then i'll add them up like would as you would just like an area of surface area of prism so the radius let's start with that your diameter here is 11 inches let's divide that by two and do want to leave it let's call it 5.5 5.5 inches know lot of people don't like improper fractions with it even though i'm i'm cool with it 5.5 inches so your start with area of base that's going to be see now want i'm going to leave this as 11 over 2. i'm gonna not use the calculator if don't have to area of base is going to be pi squared which is pi times 121 over 4 which is 121 pi over 4. that is in square inches so see can do that without calculator squared the 11 squared the two can do that without calculator leave it like that and like the exact format of that little more that's that's personal thing all right there's the area of the base so let's kind of pocket that one to the side change the color though don't want to get too blind and blue with my previous problem all right the lateral area lateral area is perimeter of base times height or circumference right parameter basis circumference perimeter of base times height is going to be 2 pi times the radius and then this is going to be all times the height the height is seven seven is the distance between your bases that's what makes the height of the prism so times seven now you this two over two two over two is one they're gone you have 11 pi times seven that's going to be 77 pi square inches so have my lateral area have the area of one of my bases let's now find the surface area by doing the lateral area plus 2 of these pi over four two over four reduces to one half so one just kind of goes away and you have two there need common denominator here so i'm gonna multiply 77 by two over two and i'm going to get 154 over 2 pi 154 pi over 2 plus 121 pi over 2 which gets me one 275 i'm getting really bad at my addition math pi over 2 square inches there's the surface area if you have the decimal version guys that should be 137.5 pi square inches believe yeah that that sounds good once again when it comes to volume we found area of base long time ago you can take area base times height you can get that volume there of that one just wait till we get to cones and pyramids and see how you feel with all this all right two more to do guys we we're gonna be dealing with both cylinders and prisms looks like they're both rectangular prisms here within and cylinder now the thing about surface area that want to make sure that you know unlike volume remember when we do volume of composite figures we add one volume with another or we subtract one volume with another the difference here and it gets little tricky the difference here is that there are some faces that get covered in surface area surface area is about what you can cover on the outside and when you look at this object right here have cylinder on top of rectangular prism and this part right here this this circle that's on top of the box this isn't exposed as part of surface this you know it's not covered as part of the cylinder mean it's it's covered with the box and that part of the box is also covered as well so the the tricky part about this will be what we take away because it's not actually part of your overall surface area don't mind calculating the initial surface area of the cylinder and the rectangular prism but the parts that we have to take away the overlap that is actually not included in the stuff that we can see on the outside is stuff we're gonna have to take out and you have to follow with me the the absolute best you can let's do one thing at time let's find the surface area of the cylinder i'll call it figure one let's find the surface area of the rectangular prism i'll call it figure two and then we'll subtract this area in the way we're supposed to you'll see what we need to do it gets tricky sometimes even myself gotta talk through it to make sure that know what to do there's not one formula to it it's however the drawing works all right so the surface area of both is going to be lateral area plus area of both bases you know so the surface area of the first one we have to find the area of the base of the first one by doing pi squared pi squared the radius is 4 feet that's going to be 16 pi square feet think we still leave our answer in terms of pi no we round to the nearest tenth but i'll leave exact answers as long as can until use the calculator so then round at that point the lateral area the lateral area of the cylinder here is going to be perimeter of base times height the perimeter being the circumference two pi and then times the height which is eight the height of the cylinder itself so 2 times 4 is 8 times 8 is 64. so i'll get 64 pi square feet like that okay so the surface area of the whole thing is going to be the lateral area plus the area of both bases like that and that's going to be exactly 64 plus 32 pi square feet now you don't combine these this doesn't become 96 pi square feet 64 doesn't have pi in it as an exact answer that's what it looks like i'll round when add these things up later when need to but have to remember to take away some stuff in the end as well in fact one of these bases that added should be taken away but i'm just getting the gist of it right just want to add these things up as if everything counted to start with hope you're okay with that all right let's find the surface area of the rectangular prism here so now that's going to be 2. so the area of the base of the second thing i'm going to call the bottom the base here that's length times width 14 times 8 and 20 12 112 square feet for one of those okay the lateral area of zebes no of the base of rectangular prism is perimeter of base times height now remember there it's 14 plus 8 plus 14 plus 8 perimeter of base times height like that 2 14 is 28 2 8 is 16 16 plus 28 is 44 44 times 12 yeah just leave it to the calculator don't want to screw this up ain't come this far 44 times 12 is 528 so 528 square feet for the lateral area so the surface area the whole thing let me box this one the surface area the whole thing there is going to be the lateral area plus the area of the two bases 112 times 2 is 224. so 528 plus is 752. there's no pie with this one so yeah these do combine so there's surface area the second one 752 square feet so the surface area of the total and this is raw total because still have to subtract something after i'll show you what i'm going to subtract but the surface area of the total guys i'm going to add these two up i'm going to take 64 plus 32 pi that's the surface area of one plus 752 that's the surface area the second one and here's what you have to subtract this circle on the base of the cylinder covers the rectangular top the the part of the surface area of the rectangular prism what that means is need to subtract that area but not just once need to subtract it twice that area that circular area is covered on both objects it's the bottom of the cylinder and it's on the top of the prism that circle is not included on either and it is included in both of these surface areas so need to take away this is this doesn't work for every single problem depends on the problem need to take away double the area of that circle and know that it's 16 pi need to take double 16 pi away good news for us is double 16 pi is 32 pi and when you add 32 pi and then subtract 32 pi well you don't have any pi left that's gone didn't know that was going to happen should have thought about that but there it is so the surface area the total thing is 64 plus 752 which believe is 816. i'd love to check all my you know answers and stuff just going through the logic unless messed up some weird math here like you know didn't do this addition right or something like that unless you did some weird math somewhere that's your surface area exactly of that whole thing that composite solid because of you subtracting that bit that we're referring to all right the the circular base that exists in the cylinder and and in the and on the prism on the prism on the top it's it's covered so it doesn't count it's not part of it all right last one here guys number eight one more composite figure to go and it's one of those it's hollowed out cylinder it's got its square kind of cut into it you know fitting square peg into into round hole kind of thing let's deal with that we'll think about what needs to be subtracted out from this thing i'm even thinking you know in in those terms right now too it's it's going to be messy no you know sometimes it's not about subtraction i'm thinking about that right now sometimes it's not about subtraction right sometimes it's about other things there there are some parts that need to be subtracted but we got to think about what what this actual drawing really is and i'll do the best can to explain it i'll tell you what net drawing is probably not going to help very much with this one because the unfolding isn't really all that it's cracked out to be because the outside isn't just the outside there's stuff on the inside as well all right but do have two objects i'm going to start with those surface areas and lateral areas and all that stuff let's see if we can make sense of that stuff to begin with got figure one got figure two figure one's big cylinder we see its radius of 14 feet don't know what that 14 has to do with guess it's that length right there so radius of 14 feet for my first object okay just so you know that's there the area the base is going to be pi squared so pi squared that's 196 pi square feet the lateral area perimeter circumference perimeter base times height so the circumference is 2 pi 2 times pi times your radius and then times the height of the cylinder that's all there are lot of 14s in this times the 14 we just saw that was 196. if you double 196 you get 392. so that's gonna be 392 pi 392 pi square feet so your your your surface area of the cylinder minus the cut out you know thing here the surface area there is going to be 392 pi plus two bases here which is 196 pi that's another 392 right that's another 392 right there so that's going to be 392 times 2 which is 784 think 784 pi square feet all right that's the surface area of should be putting on one here surface area of this cylinder minus the cut out rectangular prism let's find out the surface area the rectangular prism and it is you know once again it's good to lay out all this other work because some of it's probably going to be used in some sort of capacity you'll see what mean the area of the base now we're talking about the the rectangular prism here it's 14 by six so the area the base length times width 14 times six 14 times 5 is 70 plus 14 is 84 so it's 84 square feet the lateral area of the base is perimeter of base times height of the prism perimeter base is 14 plus 6 plus 14 plus 6 so 2 14s 28 plus 2 6 is 12 28 plus 12 is 40. so perimeter of base i'll write it out 14 plus 6 plus 14 plus 6 times the height think that was still 14 right yeah the height of the prism is 14 right there lot of 14s did say 40 before so 40 times 14 14 times 4 is 56 times 10 is 560. so 560 square feet you can see why don't want to do two more problems after this sorry you can't see it 560 square feet so have the area the base in the lateral area the surface area the whole thing honestly don't think need the surface area the whole thing but i'm just writing it anyway surface area the whole thing is 560 plus 284s at some point you might see me write that is this and then 2b is that you know i'll just write it straight up but sometimes write inside the work here as well 284 let me do this don't want to screw this part up in the end and honestly don't think need this part do need those two times 84. 728 728 square feet okay got surface area the second one surface area the first guy now everything else that's written out there is it's great i'm going to need some of the stuff because here's what we need we're not just going to add these two things up or listen we're not just going to subtract them either what you need to understand with surface area is literally it's the area of the surfaces think about what the cylinder can take without the box cut into it think about what the cylinder contains there's rectangular facing on the outside because unfolded we talked about the lateral area and then there's the area of the circles on top and bottom now when we cut rectangular prism out of the cylinder you suddenly get an opening right here that hole that is no longer part of the area of the circle the area of that rectangle the area of that base is no longer part of the circle's area so that has to be subtracted and there are two of them there's one on top and there's one on bottom so those have to be subtracted from the cylinders surface area but here's the tricky part now that's been hollowed out you see these walls you see that wall going down right here in purple and this wall on the side and on the front and on that side right there what what would ideally be these four the the lateral facings of your rectangular prism those are part of your surface area think about it that's on the inside that's something that you'd have to paint or wrap or whatever it's hollowed out that's part of surface area that has to be added that has to be added as part of your surface every total thing know this is confusing especially because don't have shape that shows it know that it is the green is going to be subtracted your two bases of your rectangular prism are going to be subtracted from the surface area of the cylinder but the lateral area of your rectangular prism the whole thing all four are actually now surfaces they're sides that are inside of it those are going to be added to the surface area so here's what i'm going to do for my surface area total don't know i'm going to write it out without plugging in the numbers first surface area of the total will be the surface area of my cylinder take away the area whoops take away the area of both bases of my rectangular prism but add the lateral area of my rectangular prism that's going to be the final thing there see there's not one formula for these guys it depends on the nature of the object and what's going on with it now it's substitution and here's the cool thing have all that information even have my 2b2 don't but it's right there have my lateral area too have my surface area 1 up here all of these are going to be used okay so 784 pi surface area of total is going to be 784 pi minus those 284s plus the lateral area of the rectangular prism which is 560. i'm going to end on this problem and that will be they said around to the nearest tenth so i'm going to do it straight up right now 784 you won't see this on my thing 784 times there's my pi bond times pi minus 2 times 84 plus 560 rounded to the nearest tenth 2 eight five five point zero zero eight six so two eight five five point zero two eight five five point zero square feet two thousand eight hundred fifty five square feet that is the surface area of the total thing there tricky very very tricky and it's conversation to be had didn't make net drawing would have been impossible for that hollowed-out thing to make sense of kind of what's there what's there and what's not but labeling everything here along the way it looks like didn't need this but labeling everything along the way is pretty useful for what it is that i'm doing there okay guys longer video with that one here whenever we're talking about surface area it's bound to happen you're going to at some point see surface area of pyramids and cones and think i'm going to make them separate videos unlike what did with volume at the time with parents and cones because they were so much the same in what we were doing these ones the formulas like to get really particular with the cone surface area as its own different thing from the pyramids even the net drying is different unlike these ones kind of have the rectangular and foldings the same those are going to be different so that ought to do it for this one guys know you're going to have some questions along the way with this if so drop it in the comment section down below i'd love to be able to try and answer as much as can but you know the video form is the thing that makes this thing best but thank you if you paid attention to it sure hope that everything came to fruition in such way that my explanation was important to make sense of how you lay out your work and how you can organize you just how you can organize this whole thing the net drawings understanding perimeter base with circumference and you know things like that can get little tricky lot trickier than volume at least and remember you will be asked to find the volume in some of these and the work that you do with areas of bases and such are really part of what's needed so it's not wasted work for you to lay that out and have it right next to when you do volume that'll do it for this one guys thank you so much this is mr robinson here take care bye