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

Answer:

Step-by-step explanation:

We have the volume of a sphere as

$V=\frac{4}{3} \pi r^3$

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

$8 =4 \pi (6^2) r'\\r'=\frac{1}{18\pi}$ ft/sec