Rate of change for volume and radius?

Question

A spherical balloon is inflated so that, when its radius is 6.50cm it's radius increases at a rate of .900 m/s

(a) Find the rate at which the volume is increasing

(b) If the change in volume is constant, at what rate will the radius be increasing when r=13.0cm

Answer 1

a) V= 4/3 pi r^3

dV/dt = 4 pi r^2 dr/dt

if dr/dt=0.9 when r=6.5 (please check units, unlikely that dr/dt=.9 m/s when r=6.5 cm, I will assume all units are cm)

dV/dt = 4 pi (6.5)^2 x 0.9

dV/dt = 477.6 cm^3/s

b) use the equation above to solve for dr/dt:

dV/dt = 4 pi r^2 dr/dt =>

dr/dt=dV/dt/[4 pi r^2]

dr/dt=477.6/[4x3.14x13^2]

dr/dt=0.225 cm/s