Gravel is being unloaded from a truck and falls into a pile shaped like a cone at a rate of 14 ft3/min. The radius of the cone base is three times the height of the cone. Find the rate (in ft/min) at which the height of the gravel changes when the pile has a height of 4 ft

0.031 ft/min

Step-by-step explanation:

Rate of unloading,  

height, h = 4ft

The formula for volume of a cone is;

Given the radius of the cone base to be three times the height of the cone;

                                       r = 3h

Substituting for r = 3h in the volume of the cone

Differentiating

Substituting the given values,

                                      ≈ 0.031 ft/min

step-by-step explanation:

rounding to the nearest thousandth would be 452,000