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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

The side of the cube is xm and side of the cube decrease by 1%.

Let, Δx denotes change in x.

Surface area of any cube is given by,

S=6 x 2

Now,

Δx= 1 100 x =0.01x

So, the change in the surface area,

dS= dS dx Δx

By substituting the given values in the above expression, we get.

dS= d( 6 x 2 ) dx ×Δx =6×2x×( 0.01x ) =0.12 x 2 m 2

Thus, the change in surface area of cube of side xmwhen side is decreased by 1% is 0.12 x 2 m 2 .


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