The volume of a sphere is increasing at a constant rate of 141 cubic feet per minute. At the instant when the radius of the sphere is 11 feet, what is the rate of change of the radius? The volume of a sphere can be found with the equation V=4/3pi r^3. Round your answer to three decimal places.

Question

Mathematics

Magdalena Jensen

16 January, 14:54

The volume of a sphere is increasing at a constant rate of 141 cubic feet per minute. At the instant when the radius of the sphere is 11 feet, what is the rate of change of the radius? The volume of a sphere can be found with the equation V=4/3pi r^3. Round your answer to three decimal places.

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Answers (1)

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Madelyn Rodriguez · Answer 1

0.093 ft/min

Step-by-step explanation:

V = 4/3 π r³

Take derivative with respect to time:

dV/dt = 4π r² dr/dt

Plug in values:

141 = 4π (11) ² dr/dt

dr/dt = 141 / (484π)

dr/dt ≈ 0.093

The radius is increasing at 0.093 ft/min.