A stone dropped into a still pond sends out a circular ripple whose radius increases at a constant rate of 3.5 ft/s. (a) how rap
idly is the area enclosed by the ripple increasing when the radius is 5 feet?
1 answer:
(a) The area is given by
... A = π·r²
The rate of change of area is the derivative of this with respect to time.
... dA/dt = π·2r·dr/dt
For the given conditions, this evaluates to
... dA/dt = π·2·(5 ft)·(3.5 ft/s) = 35π ft²/s ≈ 109.96 ft²/s
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