A stone is dropped into a quiet lake and ripples move in circles with radius increasing at a speed 4 cm/sec. At the time when the radius of a circular wave is 10 cm, find the rate at which the area enclosed by the Waves increases.
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Answer:
rate at which the area enclosed by the Waves increases =80π cm²/sec
Step-by-step explanation:
Area of a circle A = π r²
r = radius
dA/dt = 2 π r dr/dt
dr/dt = 4 cm/sec radius increasing at a speed 4 cm/sec
we need to find dA/dt when the radius of a circular wave is 10 cm
=> r = 10 cm
=> dA/dt = 2 π * 10 * 4
=> dA/dt = 80π cm²/sec
rate at which the area enclosed by the Waves increases =80π cm²/sec
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