The relative error in the dertmination of the surface area of a sphere is `alpha`. Then the relative error in the determination of its volume is :

Options

A. `(2)/(3)alpha`
B. `(2)/(3)alpha`
C. `(3)/(2)alpha`
D. `alpha`

Answer

C

Explanation

`"Relative error in Surface area, "(Deltas)/(s)=2xx(Delrar)/(r)=alpha and " relative error in volume, "=(Deltav)/(v)=3xx(Deltar)/(r)`
`therefore" Relative error in volume w.r.t. relative error in area, "`
`(Deltav)/(v)=(3)/(2)alpha`