Question

A spherical balloon is inflated so that its volume is increasing at the rate of 2.9 cubic feet per minute.

How rapidly is the diameter of the balloon increasing when the diameter is 1.4 feet?

Answer 1

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Answer 2

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Answer 3

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 = 2.9 ft³/min

πD²/2 dD/dt = 2.9
dD/dt = 5.8 / (πD²) ft/min

When D = 1.4 ft
dD / dt = 5.8 / ( π 1.4² ) ft/min = 0.9419 ft/min