Question

A right circular cylinder is changing shape. The radius is decreasing at the rate of 2 inches/second while its height is increasing at the rate of 5 inches/second. When the radius is 4 inches and the height is 6 inches, how fast is the
a) volume changing (V=(pi)r^2h)
b) surface area changing (S=2(pi)rh)

Answer 1

dV/dt = πr^2 dh/dt + 2πrh dr/dt
plug in the given values

SA = 2πrh , are you not considering the ends ?

differentiate with respect to t using the product rule like I did for the volume, then plug in the values

Answer 2

64(pi)