Wheat is poured through a chute at the rate of 14 ft^3/min and falls in a conica

Question

Wheat is poured through a chute at the rate of 14 ft^3/min and falls in a conical pile whose bottom radius is always half the altitude. How fast will the circumference of the base be increasing when the pile is 16 ft high?
Enter the exact answer. The circumference of the base is increasing at a rate of Answer units ft/min Wheat is poured through a chute at the rate of 14 ft^3/min and falls in a conical pile whose bottom radius is always half the altitude. How fast will the circumference of the base be increasing when the pile is 16 ft high?
Enter the exact answer. The circumference of the base is increasing at a rate of Answer units ft/min Wheat is poured through a chute at the rate of 14 ft^3/min and falls in a conical pile whose bottom radius is always half the altitude. How fast will the circumference of the base be increasing when the pile is 16 ft high?
Enter the exact answer. The circumference of the base is increasing at a rate of Answer units ft/min

Explanation / Answer

h=2r

When h=16,r=8

V=(1/3) r2h

V=(1/3) *2r3

dV/dt=2r2(dr/dt)

14=2(82)(dr/dt)

dr/dt=14/(128)

Circumference,C=2 r

dC/dt= 2 (dr/dt)

dC/dt=2(14/128)

dC/dt=7/64ft/min

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