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A pebble is dropped into still water, producing circular ripples that expand outward at a rate of 3.5 cm/s. When the ripple radius reaches 7.5 cm, what is the rate at which the area enclosed by the circle is increasing?
- 32.5 π cm²/s
- 31.5 π cm²/s
- 52.5 π cm²/s
- None of these
Correct answer: 52.5 π cm²/s
Solution
A=pi*r^2 so dA/dt = 2*pi*r*(dr/dt) = 2*pi*(7.5)*(3.5) = 52.5*pi cm^2/s.
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