Question

A spherical balloon is inflated at the rate of 5 cubic feet/minute. What is the volume of the balloon if when the radius is increasing at the rate of 3 feet/minute?

Answer 1

dV = surface area * dr
for a sphere
dV = 4 pi r^2 dr

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

5 = 4 pi r^2 (3)

r^2 = 5/(12 pi)

Answer 2

Volume=4/3 PI r^3

dV/dt=5=4 PI r^2 dr/dt

you are given dr/dt = 3ft/min
and dv/dt=5ft^3/min

solve for r, and then calculate V