Calculus Related Rates Question

Question

The radius of a sphere is increasing at a constant rate of 7 feet per second. At the instant when the volume of the sphere is 274 cubic feet, what is the rate of change of the volume? The volume of a sphere can be found with the equation V=4/3π(r)^3. Round your answer to three decimal places.

1

Answer 1

dV/dt = 4/3π·3r²dr/dt = 4πr²dr/dt

To get r we have 4/3πr³ = 274, so r = (137·3/(2π))^1/3 = (411/(2π))^1/3

^{dV/dt = 4π(411/(2π))^(2/3)·7 = 1428.069 ft^3/s}