This is a calculus chain rule question

Question

Air is being pumped into a spherical weather balloon. At any time t, the volume of the balloon is V(t) and its radius is r(t). 

 

a.) What do the derivatives dV/dr and dV/dt represent?

 

b.) Express dV/dt in terms of dr/dt

Answer 1

V = (4/3)(pi)r³

 

dV/dt = 4(pi)r²(dr/dt)

 

dV/dt is the rate of change of volume with respect to time

dr/dt is the rate of change of radius w.r.t. time