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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

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Answer:

Step-by-step explanation:

We have the volume of a sphere as

[tex]V=\frac{4}{3} \pi r^3[/tex]

Differentiate with respect to t

[tex]V' = 4 \pi r^2 r'[/tex]

where V' = rate of change of volume = 8

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

Substitute r=6 to get

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

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