Question

A stone is dropped into a lake, creating a circular ripple that travels outward at a speed of 60 cm/s. Find the rate at which the area within the circle is increasing after each of the following.

(a.) after 1s
(b.) after 4s
(c.) after 6s

Answer 1

`A = \pi r^2 \\ \\ (dA)/(dt) = 2 \pi r (dr)/(dt) \\ \\ (dr)/(dt)=60 \\ \\ r(t) = 60 t \\ \\ (dA)/(dt) = 2 \pi (60t)(60) \\ \\ (dA)/(dt) = 7200 \pi t`

For part a,b,c sub in value for t to get rate that Area is increasing.