Question

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

Answer 1

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 4608 square inch per minute when r=24 inches.

The rate changes because it is related to both dr/dt and dV/dr, the latter of which is not constant.