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 x m 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 x mwhen side is decreased by 1% is 0.12 x 2   m 2 .

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