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Question

Find the approximate change in the surface area of a cube of side x metres caused by decreasing the side by 1%.

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Solution

Let y be the surface area of the cube.

y=6 x2We have xx×100=1Now,dydx=12xy=dy=dydxdx=12x×x100=0.12 x2 m2Hence, approximate change in the surface area of the cube is 0.12x2 m2.

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