Question

the circular ripple caused by dropping a stone in a pond is increasing in area at a constant rate of 20 square meters per second. Determine how fast the radius of this circular ripple is increasing when the area of the circular region is 25 pi

Answer 1

2/π ≈ 0.637 m/s

Explanation:

The rate of change of area with respect to time is ...

A = πr²

dA/dt = 2πr·dr/dt

Filling in given values in the above equations, we can find r and dr/dt.

25π = πr² ⇒ r = 5

20 = 2π·5·dr/dt

dr/dt = 20/(10π) = 2/π . . . . meters per second

The radius is increasing at the rate of 2/π ≈ 0.637 meters per second.