A balloon which always remains spherical, is being inflated by pumping in 900 cubic centimetres of gas per second. Find the rate at which the radius of the balloon is increasing when the radius is 15 cm.

Explanation

`V=frac{4}{3} pi r^{3}`



`therefore` Rate af change of volume `(V)` with respect to time `(t)` is given by, `frac{d V}{d t}=frac{d V}{d r} cdot frac{d r}{d t}` [By chain rule]



`=frac{d}{d r}(frac{4}{3} pi r^{3}) `


`=4 pi r^{2} cdot frac{d r}{d t}`



It is given that `frac{d V}{d t}=900 {cm}^{3} / {s}`.


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