Question

A right cylinder has a fixed height of 6 units find the rate of change of the total surface area A with respect to r.

Answer 1

surface area of cylinder:

$A=2\pi rh+2\pi r^2$

we have: $h=6$

then:

$A=12\pi r+2\pi r^2$

rate of change of the total surface area:

$dA/dr=12\pi+4\pi r$