4. Find the approximate change in the volume V of a cube of side x metres caused by increasing the side by 1%.

Answers (1)

Side of cube increased by 1% = 0.01x m
Volume of cube = x^3 \ m^3 
we know that \Delta y is approximately equal to dy
So,
dy = \frac{dy}{dx}.\Delta x\\ dy =3x^2(0.01x) \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ (\because y = x^3 \ and \ \Delta x = 0.01x)\\ dy = 0.03x^3
Hence, the approximate change in volume V of a cube of side x metres caused by increasing the side by 1% is 0.03x^3 \ m^3

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