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
Accepted Solution
A:
Answer: 2/π ≈ 0.637 m/sStep-by-step explanation:The rate of change of area with respect to time is ... A = πr² dA/dt = 2πr·dr/dtFilling 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 secondThe radius is increasing at the rate of 2/π ≈ 0.637 meters per second.