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12-02-2018
Mathematics

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The radius r of a circle is increasing at a rate of 7 centimeters per minute. (a) find the rate of change of the area when r = 12 centimeters.

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12-02-2018

dr /dt = 7

A = pi r^2

dA / dr = 2pir

dA/dt = dA/dr * dr/dt = 2pir * 7 = 14pir

when r = 12 rate of change of the area = 14*pi*12 = 168pi

= 527.79 cm^2 / minute to nearest hundredth

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