Question

What happens to a cylinder’s surface area if its radius is squared?

Answer 1

Surface is multiplied by `(2(2r+h))/(r+h)`, or is increased by `6pir^2+2pirh`. `r`=original radius

Explanation:

`"Surface area of a cylinder"=2pir^2+2pirh`

After doubling radius:
`"Surface area of new cylinder"=2pi(2r)^2+2pi(2r)h=8pir^2+4pirh`

`(8pir^2+4pirh)/(2pir^2+2pirh)=(2(2r+h))/(r+h)`

So, when the radius is doubled, the surface area is multiplied by `(2(2r+h))/(r+h)` where `r` is the original radius.

`(8pir^2+4pirh)-(2pir^2+2pirh)=6pir^2+2pirh`, the surface area increases by `6pir^2+2pirh` where `r` is the original radius.