Surface area of cylinders formula Grade 8 TX Khan Academy

we're told the dimensions of cylinder are shown in the diagram fair enough so the radius of the base which is going to be the same as the radius of the top is 3 the height is 5 what is the lateral surface area of the cylinder pause this video and try to figure this out before we do this together and it's okay if you use calculator for this one all right now let's do this together so the first thing is what do they even mean by lateral surface area well when you're referring to the lateral of anything you're referring to its side or it's related to the sides so we're talking about the surface area if we're going around this cylinder so all the way in the backside but essentially the total surface area without the base and without the top right over there so if you imagine well that just imagine it without top or bottom that's the surface area we care about now you might have seen some different formulas here where lateral surface area is equal to the perimeter of the base times the height and in this situation what is the perimeter of the base when the base is circle the perimeter of circle is pi * its diameter or Pi * 2 * its radius or 2 pi so we're talking about cylinder like like this this perimeter of the base is going to be the same thing as two piir and then we're going to multiply that times times the height now why does that make sense that we could take the perimeter of the base and multiply it by the height in order to get the lateral surface area well imagine if we were to cut this cylinder right over here and if we were to open it up then it would look something like this it would look something like this where the height here is still 5 and the perimeter of that base would now be stretch out like this and so then it makes sense we're just taking the area of rectangle in this situation the perimeter of the base times the height perimeter of the base times the height so let's just do that right over here so the perimeter of the base is going to be 2 pi what's our radius it is three * 3 and then what is our height we've already talked about that it is 5 so times 5 so this is going to be equal to 2 * 3 * 5 * pi so it's 6 * 5 so that's 30 Pi which is the answer but it looks like they want us to have number without writing something times pi so could get calculator out and my calculator has pi button on it but they want us to use 3.14 4 Pi so let me just do 30 times 3.14 which is equal to and they want us to round to the nearest 10th didn't even have to Round Here here 94.2 so this is approximately 94.2 and we're now dealing with square meters and we are done and if someone said what is the total well then you would add the area of the top and the bottom sometimes you might see formula like this the total surface area especially if you're dealing with cylinder well then it's going to be 2 pi RH or sometimes you might see that in different orders it might be well I'll just to this right over here plus two times the area of the base because that'll take into account the base and the top so the area of each of them are pi squar this might look complicated but once again this is the one we just dealt with and then this is just adding the areas of the top and the bottom to it like to always just reason through it without having to memorize formulas because you're probably going to forget these formulas but it's really important to know where the formulas come from