A spherical balloon is inflated so that its volume is increasing at the rate of 2 ft3/min. How rapidly is the diameter of the balloon increasing when the diameter is 1.7 feet?

According to the question requirements

v = 4/3*pi*r^3

dv/dt = 4*pi*r^2*dr/dt

when

d = 1.7

r = 0.85

and

dv/dt = 2

2 = 4*pi * (0.85) ^2*dr/dtthus the the speed of increasing of the balloon's diameter is

dr/dt = 1 / (2pi * (0.85) ^2)

= 0.2203 ft/min