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

The area of a circle `(A)` with radius `(r)` is given by `. A=pi r^{2}`


Therefore, the rate of change of area (A) with resect to time `(t)` is given by,


`frac{d A}{d t}=frac{d}{d t}(pi r^{2})=frac{d}{d r}(pi r^{2}) frac{d r}{d t}=2 pi r frac{d r}{d t}`


[By chain rule] It is given that



`frac{d r}{d t}=5 {cm} / {s}`.


Thus, when `r=8 cm`,



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