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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

Verified Answer :

wizard123

\(A = \pi r^2 \\ \\ \frac{dA}{dt} = 2 \pi r \frac{dr}{dt} \\ \\ \frac{dr}{dt}=60 \\ \\ r(t) = 60 t \\ \\ \frac{dA}{dt} = 2 \pi (60t)(60) \\ \\ \frac{dA}{dt} = 7200 \pi t\)

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

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