The surface are of a balloon being inflated changes at a constant rate. If initially, its radius is3 units sand after 2 seconds, it s 5 units, find the radius after t seconds.

Explanation

Surface area of sphere, `A=4 pi r^{2}`


Given `frac{d A}{d t}=K t`



`Rightarrow=4 pi 2 {r} cdot frac{{dr}}{{dt}}={kt}`


`Rightarrow 8 pi int {rdr}={k} int {tdt}`


`Rightarrow 4 pi {r}^{2}={kt}^{2}+{c}`


`{t}=0 Rightarrow {r}=3`


`therefore 4 pi times 9={c} `


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