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Question

If there is an error of a% in measuring the edge of a cube , then find the percentage error in its surface area?

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Solution

Let x be the length of the cube.

Therefore, error in length x=dx=a% of x =a100x

Let y be the surface area of the cube, then

y=6x2dydx=12xdy=12xdx

Therefore, percentage error in the surface area is

dyy×100=12xdx6x2×100=2x×ax100x×100=2a%

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