A spherical balloon is deflating, with its radius decreasing at a constant rate of 15cm/min. The document calculates that when the balloon's radius is 9cm, the rate at which air must be removed is 4860π cm^3/min in order for the radius to decrease at the given rate. It uses the formula for the volume of a sphere and takes the derivative of volume with respect to time to determine the required rate of air removal.

1. Page 223 Problem 15 Jordan Weinberg

2. The Problem A spherical balloon is to be deflated so that its radius decreases at a constant rate of 15cm/min. At what rate must air be removed when the radius is 9cm.

3. Given Solution Volume of a sphere: 4/3 Π r^3 dr/dt=15 r=9

4. Step by Step Solution dv/dt= 4/3 Π r^3

5. Step by Step Solution dv/dt= 4/3 Π * 3r^2(dr/dt)

6. Step by Step Solution dv/dt= 4/3 Π * 3(81) (15)

7. Step by Step Solution dv/dt= 4860 Π cm^3/min