Find the surface area of a sphere when its volume is changing at the same rate as its radius.

Explanation

We know that,

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

Differentiating both sides w.r.t. `t`

`(dV)/(dt)=4*pi*r^2*(dr)/(dt)`


`(dV)/(dt)=(dr)/(dt)`


`(1-4pir^2)(dr)/(dt)=0`


`r^2=frac{1}{4pi}`


We know that, `S=4pir^2`

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