Question

A spherical balloon is inflated at a rate of two cubic feet per minute. How quickly is the radius expanding when there is already 4π/3 cubic feet of air in the balloon?

Answer 1

2/π feet per minute

Explanation:

V = (4/3)π×r³

dV/dr = 4π×r²

When V = 4π/3, r = 1

dV/dr = 4π

dr/dt = dr/dV × dV/dt

= 1/4π × 2

= 2/π feet per minute