A spherical balloon is inflated so that its volume is increasing at the rate of 3.9 ft3/min. How rapidly is the diameter of the balloon increasing when the diameter is 1.3 feet?

Question

Mathematics

Johns

1 November, 05:23

A spherical balloon is inflated so that its volume is increasing at the rate of 3.9 ft3/min. How rapidly is the diameter of the balloon increasing when the diameter is 1.3 feet?

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London · Answer 1

The volume of the sphere is obtained by the formula,

V = πD^3/6

Differentiating both sides in terms of time will give,

dV/dt = (0.5 πD^2) dD/dt

Given that the volume is changing at a rate of 3.9 ft^3/min and the diameter is 1.3 ft. dD/dt is obtained by simplifying the equation

3.9 ft^3/min = (0.5 π (1.3^2)) dD/dt

Thus, dD/dt is approximately 1.469 ft/min.