The volume of a sphere is increasing at the rate of `3` cubic centimeter per second. Find the rate of increase of its surface area, when the radius is `2 cm`.

Explanation

We know that volume of sphere:

`V = (4)/(3) πr^3`

Differentiating w.r.t. `t`


`(dV)/(dt) = (4)/(3) π 3r^2 (dr)/(dt)`

`(dV)/(dt) = 4πr2 (dr)/(dt)`` ....(1)`


Given that

`(dV)/(dt) = 3` cubic centimetre per second

`r = 2 cm `


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