Math Drills Volume and Surface Area of Prisms

hi everyone this is Mr West and today we're doing math drills tutorial video on volume and surface area of prisms so for this exercise we have four different shapes these are rectangular prisms and we need to find the surface area and volume of these various 3D shapes let me go ahead and start with the third one I'm going to explain what is the process for finding the surface area and volume first off what is surface area well surface area is kind of how you would suspect it be calculated and that is finding the area of all the different surfaces so we have this green surface we have this blue surface in this purple surface and we're going to add those all together so you can see here kind of had this template set up already now one thing you're going to want to note is because it's 3D shape we're going to have two purple areas okay so we have this area right here that's on the top but also this one on the bottom so it's kind of tough to imagine 3D shapes so we're going to have to be very careful as we do these calculations so there's one green side right here but there's also one in the back and then we have this front blue surface and then also one in the back so these are called faces and three three-dimensional rectangular prism has six cases so we're going to have to keep that in mind as we calculate the total surface area now one of the things we're going to need to know also is how to calculate the area of any shape so for this one these are all rectangles or squares and the formula for rectangular square is pretty simple we just have to do the length times width so that's going to make it easier for us so we're going to go ahead and start might as well go in order with the green one oops so here's the green one we know that and this is what would recommend is just redrawing the shape so I'm going to draw it off to the side we have this shape it's long green rectangle and we know it's three centimeters by one centimeter so if we're going to do length times width area equals length times width sorry got to squeeze that in there it's going to be area equals three times one very simple here it's just going to be three and now we need to get the units correct it's centimeter Square so we're technically multiplying centimeters by centimeters so that gives us our area unit which is centimeters squared so we have one of those I'm going to go ahead and write that in three centimeters squared but the thing is like said earlier we have two of those so any time we're going to do the surface area for these rectangular prisms if we find the area of one of the faces we know there's going to be an identical one so really we just need to calculate the green the purple and the blue and we multiply each one of those calculations by two so I'm going to multiply this by two just like that or we could add them up and multiply put two by the end it doesn't matter because the distributive property but I'm going to go ahead and just show you that all the green surface is going to be six centimeters squared all right so we're done with the green we know that this whole face and that whole face on the back side adds up to six centimeters squared so now we're going to do the purple that one's the next on our list and we see that we have one by one square so figuring out the dimensions of the rectangular prism is kind of the tough part sometimes you have to be very careful recommend redrawing the shape so we see it's one centimeter by one centimeter this one's going to be even easier we have one times one that just gives us one centimeter squared for our area so we write one centimeter squared there's two of those one on the top one on the bottom so then that equals two centimeters squared now we're moving on to the blue so the blue is just like the green okay the dimensions are three by one so we have three by one kind of ran out of room here and then we have area equals length times width so that's three times one and we got three centimeters squared again so we have three centimeters squared and as you can imagine if we multiply that by two we also get six centimeters squared so what I'm going to do here is I'm just going to add these all up so these three numbers this is the total surface area Okay so those are all the faces that's the area of all the green faces all the purple and all the blue add those up so get 6 plus 2 is 8 plus 6 is 14 centimeters squared and that's my surface area so is 14 centimeters squared okay now moving on to volume I'm going to erase all this volume's little bit different now volume we're talking about three-dimensional space how much space is taken up so not just the surface think surface area if we wanted to paint something so if we wanted to paint something we'd only be painting the surface how much paint would we need to cover that two-dimensional surface 3D is like we're filling it with water or some liquid or material so for 3D this is the process we just want to calculate how many cubic units of space we have so you can kind of see we have these it's kind of little bit tricky here but we have like this unit right here that would be one cubic unit that we could fill in right there and how many can we fit in this whole little prism well in this prism it looks like we got second one so that's one two and then this top one would be three that's three centimeters cubed three cubic centimeters how many little cubes cubic units can we fit inside our shape so that's how you calculate the simple way to calculate volume is cubic units now what's the process well the process if you didn't want to just count would be length times width just like we did for area but then we ultim also multiply by the depth essentially what you're doing is you're multiplying the three dimensions together and how's that work out for this one well for this one our length and width we already knew we could call it one times three and then we multiply it by the depth the third dimension and this was also one so one times three times one gives us three and then we multiplied three dimensions together so that's why it's centimeters cubed centimeters times centimeters 10 centimeters is centimeters cubed so that's the whole process if you understood that then you can apply it to all these problems I'm going to go ahead and do it to the second one okay and what I'm going to do is I'm just going to copy and paste this right here I'm going to use this template think this is great to use for surface area surface area honestly takes lot longer than volume volume is the easier of the two but yeah so let's go ahead and get started so here we have the green we're going to start by redrawing it this is my recommended first step and it's seven by seven so seven by seven if multiply those together so area equals 7 times 7 and that is 49 inches this time squared so have 49 and I'm going to show you different way to do it I'm just going to go one of these and then I'll multiply by 2 at the end okay so then my next one is purple okay and that's seven by one so have this little rectangle right here I'm just going to kind of label like that this is seven that's one and do seven times one that gives me seven inches squared so now have seven inches squared and then have another blue one okay I'm just going to put it over here next to it and you can see that this is seven by one also so that's going to give me seven inches squared seven inches squared so what I'm going to do is be careful here only did one of the two faces for each color so I'm going to add these all up this is just the second way to do it if you want just multiply them by two and then add those up I'm going to show you can do the same thing so different way so we're going to add 49 plus 7 plus 7 that gives me 63. inches squared but also have to multiply it by two because those are only one of the faces so multiply that by two and get 126 inches squared if you were to multiply each one of these by two first you'd get the same thing so that would give you 98 plus 14 plus 14 you get the same thing you get 126. so that's just two different ways to do it but 126 inches squared make sure you have the correct units on this is our answer volume this is going to be little different now volume and keep this color we're like said we could just count all these cubic units we have one two three four five six seven eight that was no seven sorry double counted this first one that's seven cubic units if were to draw it okay seven cubic units and could just do that again seven times think so we just kind of drawn these out okay so you could go around and count them that's one way to count these cubic units if you were to stack all these together or you can do volume equals length times width times depth so I'm going to do 7 times 7 times 1 and you're going to see that we get 49 inches cubed so we get 49 inches cubed for this there's 49 of those little cubes in there okay so that's the process think we probably have time for one more we'll just leave number two out of this for today if you have question leave it in comment but for this last one we're going to go ahead and kind of take the quick process for this so again would recommend posting this little template or at least writing this out having the green area and maybe if you have pencil you might not have colored pencils you could do green area and then purple area and you might not even have colors for this so you could just go top area or bottom area just label the different faces so you know or you could call it this small area or the the right area and then the left area we'll call this one the left area and then we'll call this the top area oops get my colors correct okay so that's what I'd recommend if you want to label them differently so don't get confused and then you can multiply these by two okay each one of these so let me go ahead and start so have this one is going to be three by three this rectangle is three by three so that's nine so have nine for this I'm not I'm going to double it at the end that's what I'm gonna do and then have the right area that's three by six again would really recommend redrawing it that's 18. I'm gonna do units at the end and then we have another three by six okay so that's going to be 18 also okay so then I'm going to add this all up that gives me 36 plus nine okay and then I'm going to multiply that by two and get 90 and then my units are inches squared for surface area 90 inches squared for volume now we're just going to multiply the three dimensions together that's essentially what you're doing length times width times depth this is for rectangular prisms so we get 9 times 6 sorry three times three should write that out three times three times six and get 9 times 6 which is 54 and then this is inches cubed so that's all there is to it hope you enjoyed this video hope it was helpful also if you have any other questions on volume or Surface area let me know also have ton of other videos for math drills or any other math drills worksheets so go ahead leave comment or do search on my YouTube channel if you need additional help like And subscribe and look forward to seeing you next time right here on West explains best