Question

Air is being pumped into a spherical balloon at a rate of 2 cubic meters per minute. Find the rate of change of the radius when the radius is 3 meters. v=4/3pir^3

Answer 1

You want to find dr/dt, given that dV/dt = 2 and r = 3.

Differentiate V = 4/3 pi r^3 with respect to time, t. Substitute what you know and solve for dr/dt.

Answer 2

so 4/3pi3r^2(dr/dt)