Question

The surface area, A, of a cylinder of radius, r, and height, h, can be found with the equation above. Which of the following correctly shows the cylinder's height in terms of its radius and surface area?

Answer 1

Explanation:

If r and h are the radius and height of the cylinder, then its surface area A is given by :

`A=2\pi r^2+2\pi rh` ....(1)

We need to find the cylinder's height in terms of its radius and surface area. Subtracting
`2\pi rh` on both sides, we get :

`A-2\pi r^2=2\pi rh+2\pi r^2-2\pi r^2\\\\A-2\pi r^2=2\pi rh`

Dividing both sides by
`2\pi r`. So,

`(A-2\pi r^2)/(2\pi r)=(2\pi rh)/(2\pi r)\\\\h=(A-2\pi r^2)/(2\pi r)`

Hence, this is the required solution.