If there is an error of `k %` in measuring the edge of a cube, then the percent error in estimating its volume is `k` (b) `3k` `k/3` (d) none of these

Options

A. `k`
B. `3k`
C. `k/3`
D. None of these

Answer

B

Explanation

We know that the volume `V` of a cube of side `x` is given by
`V=x^(3)`
`(dV)/(dx)=3x^(2)`
Let the chagne in `x` be `Deltax=k%` of `x=(kx)/100`
Now, the change in volume
`DeltaV=((dV)/(dx))Deltax=3x^(2)(Deltax)`
`=3x^(2)((kx)/100)=(3x^(3).k)/100`
`:.` Approximate change in volume `=(3kx^(3))/100=(3k)/100 . x^(3)`
`=3k%` of original volume.