Air is being pumped into a spherical ball, at the rate of 10cm^3/min. Find the rate of change of the radius of the ball, when the radius is 15cm.

Question

I've tried working it out using the formula for volume, but I am not getting the answer I want. I am hoping someone could possibly show me with the work and the answer along with it.

Answer 1

Assuming you are working with the formula:

V = 4/3 πr³, then differentiating implicitly with respect to t (time) you should get something like this:

dV/dt = 4 πr² dr/dt.

Now substitute what you know and solve for dr/dt.

dV/dt = 10cm³/min

r = 15 cm

10 cm³/min = 4π(15)² dr/dt

You take it from there.