A stone is dropped into a quiet lake and waves move in circles at a speed of 4cm per second. At the instant, when the radius of the circular wave is 10 cm, how fast is the enclosed area increasing?

Explanation

`{dr} / {dt}=4 {cm} / {sec} ldots text { (i) }`



As we know that the area of the circle is `pi r^{2}`



`frac{{dA}}{{dt}}=frac{{d}(pi {r}^{2})}{{dt}} `


`Rightarrow frac{{dA}}{{dt}}=pi frac{{d}({r}^{2})}{{dt}} `


`Rightarrow frac{{dA}}{{dt}}=pi times 2 {r} frac{{dr}}{{dt}} `


`Rightarrow frac{{dA}}{{dt}}=2 pi r times 4 ldots ldots` .


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