A stone is dropped in to a pond causing ripples in the from of concentric circle . the radius r of the outer ripple is increasing at a constant rate at 2cm per second . when the radius is 5cm find the rate of changing of the total area of the disturbed water
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Rate at which the area enclosed by the Waves increases =20π cm²/sec at 5 cm radius when radius of ripple is increasing at a constant rate at 2cm per second
Step-by-step explanation:
Area of a circle A = π r²
r = radius
dA/dt = 2 π r dr/dt
dr/dt = 2 cm/sec radius increasing at a speed 2 cm/sec
we need to find dA/dt when the radius of a circular wave is 5 cm
=> r = 5 cm
=> dA/dt = 2 π * 5 * 2
=> dA/dt = 20π cm²/sec
rate at which the area enclosed by the Waves increases =20π cm²/sec
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