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

1 Answer
Mar 16, 2018

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.