Question

The radius, r, of a sphere is increasing at 0.03 meters per second. The rate of increase is constant.

Answer 1

A)
Given: dr/dt = .03 m/s and r = 18 m
Volume of a sphere = (4/3)*PI*r^3
Take the derivative of both sides, so
dv/dt = 4*PI*r^2*dr/dt
Plug in the givens and you have the rate of increase of the volume
B)
Given: V = 288 m^3 and I'm going to assume that r and dr/dt are the same as in part A
Surface Area = 4*PI*r^2
Take the derivative on both sides, so
dA/dt = 8*PI*r*dr/dt
Again, plug in the givens and you'll have the rate of increase in the surface area
C)
This part, it's been awhile since I've done related rates, so it may take me awhile, but perhaps the next person can answer it before I finish.