Question

The radius of a sphere is increasing at a rate of 3 inches per minute.

a. Find the rate of change of the volume when r = 9 inches.
b. find the rate of the circumference when r = 9 inches.

Answer 1

AP Calc.

Answer 2

\[V=4/3 \pi r^3\] take derivative w.r.t t on both sides:
\[dV/dt= 4 \pi r^2 (dr/dt)\]
when r=9 (dr/dt)=3 , dV/dt= 4*pi*81*3

for part b use same method on \[C=2\pi r\]

Answer 3

You sir, are a life saver! I didn't get any of this stuff! Thanks so much!