Volume：The radius r of a sphere is increasing at a rate of 2 inches per minute

题目

Volume：The radius r of a sphere is increasing at a rate of 2 inches per minute
Find the rate of change of the volume when r=6 inches and r=24 inches
Explain why the rate of change of the volume of the sphere is not constant even though dr/dt is constant

答案

V=Volume=4π(r^3)/3,dV/dr=4π(r^2),so the rate of change of the volume, dV/dt=(dV/dr)*(dr/dt)=4π(r^2)*2,then you can calculate the value of dV/dt is 288 square inch per minute when r=6 inches,and 460...