The error in measuring the side of a cube is `pm1%`. The error in the calculation of the volume of the cube will be about

Options

A. `pm 0.001 %`
B. `pm 1%`
C. `pm 6%`
D. `pm 3%`

Answer

D

Explanation

Volume of cube V = `("side")^(3)`
`therefore V = a^(3)`. Take log and differentiate.
`(Delta V)/(V) xx 100 =3 (Delta a)/(a) xx 100 = 3(pm 1%) = pm 3%`