Question

A spherical balloon is inflated so that its volume is increasing at the rate of 3.1 {\rm ft}^3{\rm /min}. how rapidly is the diameter of the balloon increasing when the diameter is 1.6 feet?

Answer 1

The volume is represented by V = volume of sphere = (4/3) π r³ = (4/3) π (D/2)³ = π D³ / 6 dV / dt = (π D² / 2) dD/dt ft³/min dV/dt = 2.3 ft³/min πD²/2 dD/dt = 2.3 dD/dt = 4.6 / (πD²) ft/min Thus when D = 1.4 ft dD / dt = 4.6 / ( π 1.4² ) ft/min = 0.7471 ft/min