6. The height h of a right circular cone is 20 cm and is decreasing at the rate of 4 cm/sec. At the same time, the radius r is 10 cm and is increasing at the rate of 2 cm/sec. What is the rate of change of the volume in cm3/sec? (Note: The volume of a right circular cone is V = 1/3p r2h.)

 

A. -400p

B. -400p /3

C. 0

D. 400p /3

E. 400p

 

 

Solution: The answer is D

To find the rate of change of the volume, V, with respect to time t, solve for dV/dt, as follows:

Given,

Differentiating with respect to t, results in the following differential equation,

 

Since,

By substitution,

Thus, when h = 20 and r = 10, the rate of change of the volume is given by,