Question

20 COINS

Cylinder A has radius r and height h as shown in the diagram. Cylinder B has radius 2r and height 2h. How many times greater is the surface area of Cylinder B than the surface area of Cylinder A?

Answer 1

The surface area of a cylinder is given by

`A_A = 2\pi rh`

which is the surface area of cylinder A.

To compute the surface area of cylinder B, we have to map
`(r,h)\mapsto (2r, 2h)` and we have the following formula

`A_B = 2\pi(2r)(2h)`

If we manipulate the second expression, we have

`A_B = 8\pi rh`

Which implies

`(A_B)/(A_A) = (8\pi rh)/(2\pi rh) = 4`