Question

Find the approximate change in the volume ‘V’ of a cube of side x metres caused by decreasing the side by 1%.

Answer 1

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%