Question

a right circular cylinder has a fixed height of 6 units. Find the rate of change of its volume V with respect to the radius r of its base. Find the rate of change of the total surface area A with respect to r.

Answer 1

$\frac{dV}{dr}=\frac{d(πr^2)h}{dr}=2πrh$

$\frac{dA}{dr}=\frac{d(2πr^2+2πrh)}{dr}=4πr+2πh=2π(2r+h)$