How to Find Volume of Prisms and Cylinders Fast

what's popping dogs Mr Allen here finding the volume of some prisms and cylinder in this video and the reason why pair all these up is because they can all follow the same formula the volume is equal to the area of my base whatever that base is rectangle triangle triangle circle multiplied by my height and Ed an uppercase for the area of that base or I'll say Big multiplied by my height and the height is just the distance between my bases we'll go over that for each one of these different examples here in moment so for this first one here have rectangular prism now common formula for this one and I'm going to do this in two different ways here would be volume equals my length time my width times my height just my three dimensions all multiplied together 12 * 8 * 10 and that's going to be let's see here 12 * 8 is 96 * 10 would be 960 so 9 60 in cubed volume is in cubed or Meers cubed feet cubed whatever the units are cubed because it's inches time inches time inches or inches to the 3 if you will all right so that is one way of finding the volume here another would be find the area of one of your rectangles so in this case let's say 12 * 8 is 96 and multiply by the distance between those other two the other rectangle up there the two bases of the prism okay that's very important characteristic of prism is it has two bases that are the same whereas pyramid or cone if we're going circles you know cylinder and Cone prism pyramid the pyramid and The Cone both come to single point whereas the prism And the cylinder have two of the same bases above each other or left or right or whatever it may be in the particular example okay so there we go first one done next one let's go to the triangle over here the triangular prism and this is right triangular prism okay so my base here my bases excuse me my bases are triangles okay it's it's common common mistake to say it's just the guy that's that's flat right that's got to be my base but there isn't another one like that there's not another one parallel to it if you will so it has to be the two bases that are identical to each other and my height my height is just the distance between those two bases so here my height is 10 even though it's like kind of horizontal it's the distance between the two triangular bases so our volume formula is still Big * let's figure out what that Big is it's triangle so here's how like to write it up so my area of triangle is my Big all right so stay organized in this way that way know I'm like it's triangle that's my base area of the triangle Big use the subscript with little shape there or you can write the actual word triangle if you're not too good at drawing shapes so area of triangle it's 1/2 base times height lower case be the length be don't have that do have however my my height of the triangle which is eight but need this length right here so what what is this length well this 17 is going to be the same as this guy right here feet this is an 8 what 17 well if you know your Pythagorean triples it's an 8 15 17 or you can set up some pythag I'll write that up real quick for you you'd have to solve it though it'll be 8^2 plus x2 in this case equal 17 squ if you solve that you would get 50 but if you know your triples and we throw lot of triples at you in these different problems here because what we're really testing you is can you do the volume but we also have little you know little extra fun with the math right got throw throw little little review math at you if you've already covered pythag baby all right so this is going to be 15 right here so now let's finish mathing this up and I'm going to try to not use my calculator here have it if need it let's see here it will be well half of 8 is 4 and 4 * 15 is 60 so this is 60 ft squared for my area of the triangle which is my Big now let's figure out my actual volume here so volume is Big volume is Big which is 60 times my height which is 10 it's going to be 600 feet cubed boom Final Answer Circle it hopefully it stayed on the board over there it did excellent all right there we go man beautiful so pythag making comeback it may happen again who knows I'm going to keep going in this clockwise motion here so let's go down to the triangle we'll finish with the cylinder the moment you're all waiting for know okay well this is an interesting one looks like my bases are going to be triangles here those are the ones that are the same again my my lateral Ed or my lateral area the part that wraps around those are all made up of rectangles you'll see that really with any of your volume formulas everything's made up with rectangles for prisms all right it's just the bases that can change shape you could have trapezoid okay you could have trapezoid there you could have parallelogram it could be anything hexagon octagon whatever all right well let's do this this is an Isles triangle because two of the sides are the same I'm going to drop down an altitude okay you could do that isos triangles the altitude also bcts the opposite side it splits this into three and three that's only true for isoceles triangles as well as equilateral triangles the altitude right will also bict that opposite side it will be drawn to the midpoint of that opposite side so three what five that's that's the that's the best one right three four five it's like the most universal Pythagorean triple people use it all the time people use it in the trades when they're squaring up walls or slabs concrete all that good stuff right they do 3 four five or they double it to eight sorry 6 8 10 so on and so forth you can multiply those triples by anything you want okay so be on the lookout for multiples of triples as well but now have my height of this triangle and can go about it in the same sort of way here I'm going to the area of the triangle that's my big which is 1/2 my base is six the height of that triangle is four so that's half of 24 is 12 feet squared and then we have our volume part I'll do that in green again match the other one volume is Big times my height the distance between these two triangles here well that's going to be 96 feet cubed nice beautiful okay note that didn't put like you can't do this this is not okay 96 fet cubed like that looks no that this right here no okay cannot cannot notate cubic feet in that way you have to do the Ft cubed or you can write cubic feet or cuu ft is also acceptable but not the little abbreviated you know Le or two for in not okay to do when you're talking about area and volume all right last one here we have cylinder okay so let's see my my big my Big in this case is circle okay so we're talking area of circle that is my Big okay my area my base for this volume formula and that is pi squ it's classic an absolute whoa whoa got my diameter here need my radius which is going to be 6 we're in metric now which was just crazy so we got Pi * my radius squared that's going to be 36 Pi squared for my area of my base I'm going to keep it in terms of Pi here then don't have to bust this guy out yet might have to in sec here let's see here okay so now my volume Big * and like this formula because don't have to that that little tail on the There is bothering me don't have to memorize all these different ones some people are like for volume of cylinder it's pi time for volume of this guy it's 1 half base time height time it's like you know one formula and you just have to know all the different area formulas then it's universal volume formula just know the different area formulas for my different shapes that was voice crack right my triangles my rectangle square parallelogram Circle trapezoid whatever they can all be thrown at you in these volume problems so like this one okay volume is Big 36 Pi * 15 okay have an idea okay think it's 36 * 10 would be 360 let's see if we can do this by hand we'll check it in sec 36 * 10 would be 360 36 * 5 that' be half of 360 which is 180 so think this is 540 Pi me cubed let's see 36 hold on we're validating my OS real quick 36 * 15 nailed it nice beautiful 540 Pi cubed if you were asked to put this into decimal you would do 540 time 2 pi on this guy here it's the little carrot button right above the division sign hit enter and then you can get 1,696 460 so 46 met cubed that' be an approximate answer right there also acceptable unless they say in terms of Pi or it's multiple choice pick whichever one is there but otherwise guys that is about it on this wonderful little intro to finding the volume of different solids different prisms and cylinder put them all in the same category cuz they all have the same formula with just changing base that's it all right thanks for watching you guys have wonderful day and make sure you like subscribe share it and if you have any questions pop it in the comics see you later