Khan Academy Tutorial volume and surface area of cylinders

welcome back to West explains best we're doing another Khan Academy tutorial today for geometry this is volume and surface area of cylinders so we're gonna be doing everything related to cylinders with this one so let's go ahead and start with this first question which is what is the volume of cylinder with base radius 2 in height of 9 one thing we'll need to understand about the formula for volume is we need to understand that it is the area of the base hold on sorry don't want to give that away is the area of the base times the height and that's true for any prism so cylinder is basically special type of prism that is circular and I'm gonna go ahead and shade my base here and then my height is gonna be 9 ok essentially what we're doing is you're taking the area of the circle and then you're pulling it all the way down this height and that forms volume so you're taking it into third dimension which is why units for volume are units cubed okay so let's get back to the task at hand well we need to understand what the area of the base is so the area of the base is going to be equal to PI squared because it's circle now we're just gonna input our value so we have pi times 2 squared we do order of operations to do 2 squared which is 4 and then multiply that by PI think it says answer exact same answer in terms of pi so that's what we're gonna do so for first one we got the area the base is 4 pi now we're just plugging our height which is 9 so we get 36 pi and that's our answer 36 pi okay next question what is the surface area of cylinder with base raised to in height of 5 surface area as it suggests as in we're talking about area so it would we're talking about two-dimensional space that's all the surface so if we were to paint this object and not fill it volume is like how much can be filled service areas everything on the outside that can be painted so we're asking what is the outside measure of all this and on the top and on the bottom so lateral area is everything that's on the side surface area includes the sides the lateral area plus the two bases because prisms and cylinders have two bases so we can derive formula for surface area as the lateral area everything that's in the side and purple plus the two bases the area of the two bases and this big means area of base let's go ahead and start with what we know we know the area of base is equal to PI squared we know the radius is 2 so we can plug that in and guess what we have the exact same area of the base so we're gonna plug in for pi but don't forget that we have to multiply that by 2 because we need two bases okay now we have our lateral area lateral area how do we think about this well if we were to unravel kind of like soup can unravel the sides of this cylinder it would form rectangle where this distance is 5 now what would this distance be equal to that's the question at hand well that distance right there is if we rolled it up it would form the perimeter of the circle or the circumference so we need to do is we need to find the circumference of this circle and then multiply it using the rectangle formula by the height which is 5 so our circumference is going to be 2 PI and then we're to multiply that by the height that's our formula for lateral area of prism 2 PI times the height well we know 2 pi times 2 razes 2 in there our height is 5 so we get 4 times 20 or 4 times 5 is 20 20 pi so now we know our lateral area is 20 pi and we can calculate the surface area by adding these two together so surface area sorry about that equals 20 pi plus 2 times 4 pi because there's two bases 8 pi so we get 28 PI square units notice how the units are squared and not cubed cubed is for when we have volume 20 8 pi check okay next question will do maybe one one or two more just so you get the hang of it what is the volume of cylinder okay we're talking about volume how much we can fill so are we already know our formula is equal to PI squared so is 3 we're going to square that first and then we're multiply that by PI and we're to multiply that by 8 so that becomes 3 squared is 9 9 pi times 8 we get 72 pi and that's our final answer usually volume is little bit easier so this is like how much how many units of water we can fill this particular cylinder with so we put 72 PI cubic units check the answer let's do one more surface area surface area we know is whoops those bad surface area is our lateral area which is 2 PI that's the circumference times the height of the cylinder or that the perimeter times the height that's what the any prism is gonna be and then we need to add as but add that plus sign to of the bases let's start with our bases our base is gonna be PI squared yep that's going to be our base when we multiply that by 2 so we have pi times 3 squared that's gonna be 9 PI let me multiply that by 2 so we have 9 pi times 2 and then we have 2 pi times 3 times our height which is 6 we're add those two together so that gives us 18 36 PI plus 18 pi that's 44 54 pi is gonna be our surface area in square units 54 pi square units hope you guys found this helpful and you have better understanding of cylinders with both volume and surface area and I'll see you next time on West explains best take care