The error in the measurement of the radius of a sphere is `1%`. Find the error in the measurement of volume.

Options

A. `1%`
B. `2%`
C. `3%`
D. `5%`

Answer

c

Explanation

If the error in x is `deltax`, then the percentage error in `x^(n)` is `n((deltax)/(x))xx100%`. For a sphere `V=(4)/(3)pir^(3)`
In this case x = r and n = 3 and `((dx)/(x))=(1)/(100)`.
`therefore` Percentage error `=3((1)/(100))xx100%=3%`