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
1 answer:
Answer:
2/π ≈ 0.637 m/s
Step-by-step 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.
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