9) The approximate change in the volume of a cube of side x metres caused by increasing the side by 3% is
(A) 0.06 x^3 \ m^3                     (B) 0.6 x^3 \ m^3                 (C) 0.09 x^3 \ m^3                     (D) 0.9 x^3 \ m^3

Answers (1)

Side of cube increased by 3% = 0.03x m
The 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(0.03x) \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ (\because y = x^3 \ and \ \Delta x = 0.03x)\\ dy = 0.09x^3
Hence, the approximate change in volume V of a cube of side x metres caused by increasing the side by 3% is 0.09x^3 \ m^3
Hence, (C) is the correct answer

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