Problem 895

The value V = $\frac{4}{3}$ πr³of a spherical balloon change with the radius.

a. At with rate (ft³/ft) dose the volume change with respect to the radius when r = 3 ft?

b. Using the rate from part a, by approximately how much dose the volume increase when the radius change from 3 to 3.3 ft?

Solution:-

a. At what rate (ft³/ft) does the volume change with respect to the when r = 3 ft?

36π ft³

b. Using the rate from part a, by approximately how much does the volume increase when the radius change from 3 to 3.3 ft?

33.93 ft³