Question

A sphere has a volume of 36π cubic
meters. The rate of change in volume is
9π cubic meters per minute. Find the
rate of change in area of the sphere

Answer 1

v = 4/3 πr^3
a = 4πr^2

dv/dt = 4πr^2 da/dt = a da/dt

So, find a when v = 36π and plug it in to find da/dt.

Answer 2

oops. forgot about r.

dv/dt = a dr/dt
da/dt = 8πr dr/dt
So, find r and a when 36π and plug them in to find da/dt