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Question

A circular metal plate expends under heating so that its radius increases by k%. Find the approximate increase in the area of the plate, if the radius of the plate before heating is 10 cm.

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Solution

Let at any time, x be the radius and y be the area of the plate.
Then, y=x2Let x be the change in the radius and y be the change in the area of the plate. We havexx×100=kWhen x=10, we getx=10k100=k10Now, y=πx2dydx=2πxdydxx=10 cm=20π cm2/cmy=dy=dydxdx=20π×k10=2kπ cm2

Hence, the approximate change in the area of the plate is 2kπ cm2 .

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