Question

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?

Answer 1

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