Question

Find the rate of change of the radius of a sphere at the moment in time when the radius is 6 feet long and the volume of the sphere is increasing at the rate of 8???? feet 3⁄second. Note: The Volume of a Sphere is given by the formula ???? = 4 3 ???????? 3

Answer 1

Explanation:

We have the volume of a sphere as

`V=(4)/(3) \pi r^3`

Differentiate with respect to t

`V' = 4 \pi r^2 r'`

where V' = rate of change of volume = 8

and r' = rate of change of radius to be found out

Substitute r=6 to get

`8 =4 \pi (6^2) r'\\r'=(1)/(18\pi)` ft/sec