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Question
Find the approximate change in the volume ‘V’ of a cube of side x metres caused by decreasing the side by 1%.
Solution
The volume of a cube
`V = x^3`
`(dV)/(dx) = 3x^2`
`:. deltax = x. 1/100 = (-x)/100`
∴ Chnage in volume
`deltaV = ((dV)/dx)deltax = (3x^2).((-x)/100) = -(3/100)x^3`
`= - 3/100V = -V 3/100`
∴ Change in volume decrease by 3%
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