Question

If you are blowing up a balloon at a rate of 3 cubic ft per min, what is the rate of change of the radius after 30 seconds

Answer 1

dV/dt = 3ft^3/min(1 min/60s) = .05 ft^3/s
so
V = .05 * 30 = 1.5 ft^3 at 30 s

V = (4/3) pi r^3
so r = 0.71 ft at 30 s

dV/dr = 4 pi r^2 (the surface area of course)
but
dV/dt = dV/dr * dr/dt
so
dr/dt = dV/dt / (4 pi r^2)

dr/dt = .05 /(4 pi*.71^2)
= .00789 feet/second

Answer 2

aren't you supposed to plug everything in AFTER you derive it?

Answer 3

LOL, either way

I do physics, I find t easier to visualize step by step.