How to Find the Surface Area of a Cylinder Math with Mr J

Welcome to Math with Mr. In this video, I'm going to cover how to find the surface area of cylinder. And remember, surface area is the total area of the outside part or layer of 3D figure. So, let's get into our example here. And on the left-hand side of your screen, we have the cylinder that we're going to find the surface area of. It has given height of 8 in and our base has radius of 3 in. Now, on the right-hand side of your screen, I'll draw an arrow to it, we have the net of that cylinder. So, we took the 3D figure and unfolded it. So, we see all the different parts that make up that cylinder as flat figure there. And this is going to help us visualize and see what parts that we're going to find the area of and then add together in order to get the surface area. So, at the top of your screen, we have the formula that we're going to use. The bottom formula here, I'll underline it. This is the official formula that we're going to use in order to find the surface area. But the top one kind of breaks it down and tells us exactly what we'll be doing. So, the top one, surface area equals two times the area of the base plus the area of the rectangle. Now, the one below it has the official formulas. So, pi squared here, that's the formula for the area of circle. Our top and bottom, the bases, are circles. And we can multiply it by two. If we find the area of one, we have the area of both because they're both the exact same. That's why we're multiplying it by two. So, find the area of one, multiply it by two. And then we have 2 pi So, 2 pi that is the formula for the circumference of circle. So, let's take look at this rectangle within our net. So, we have the height here. That's going to match our 8 in. So, that rectangle has height of 8. Now, this side length is going to be the circumference of our base circles there. So, if we took the circle and kind of folded it down and made it flat line, it would match this side of the rectangle exactly. So, that's why we have circumference within the formula for the area of that rectangle. So, we need to find the circumference, multiply it by the height, and we have the area of the rectangle. So, let's plug in all the information we have, solve, and get the correct surface area here. So, we will start by rewriting our formula, surface area equals 2 pi squared plus 2 pi So, now we plug in. So, 2 pi, the radius is 3 squared plus 2 pi radius is 3 of our base again times the height of 8. And we can start simplifying this and work our way down to the correct answer. So, let's do 3 squared here, which is 9. times 2 is 18. So, we end up with 18 pi plus let's do 3 times 8 is 24 times 2 is 48. So, we get to 48 pi on this side. So, we have 18 pi plus 48 pi. So, that's going to give us 18 plus 48 is 66. So, we get to 66 pi. And I'm going to use the pi button on calculator in order to find this final answer. If you use the approximate or rounded version of pi, 3.14, 3 and 14 hundredths, that's very common to do. Your answer may be slightly different than mine, but it is correct. You just used the rounded version of pi. I'm using the button on the calculator, which is the more extended version of pi. So, once plug that in, I'm going to come to the right where have more room. get surface area equals 207 and get very long decimal. So, I'm going to round this to the nearest hundredth. So, get 35 hundredths, .35. And this is surface area and we're working with inches, so it's square inches. So, we get final answer of 207 and 35 hundredths square inches. So, there you have it. There's how you find the surface area of cylinder. We find the area of the base, the circular top there. We multiplied it by two because we have two circles. And we added that to the area of the rectangle. And we end up with, for this particular example, 207 and 35 hundredths square inches. hope that helped. Thanks so much for watching. Until next time, peace.