A spherical balloon is inflated with a gas at a rate of 20 cubic feet per minute. How fast is the radius of the balloon changing at the instant the radius is 1 foot is the formula for volume is

Question

V=(4/3)∏r^3?

Would not let me type the whole equation above, but this is the formula for volume. I was confused on how to solve this type of problem.

Answer 1

Goal is to find dR/dt when r=1

V = 4/3 * pi * r^3

dV = 4 * pi * r^2 * dR/dt

20 = 4 * pi * 1 * dR/dt

20 = 4 * pi * dR/dt

20/(4*pi) = dR/dt

5/pi = dR/dt