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. `(3)/(2)alpha`
B. `(2)/(3)alpha`
C. `alpha`
D. `(5)/(2)alpha`

Answer

A

Explanation

Surface area of sphere is `S= 4pi r^(2)`
`(triangleS)/(S)=2xx(triangle r)/(r )=alpha`
`implies (triangle r)/(r )=(alpha)/(2)" ""………….."(i)`
Volume of sphere `v=(4)/(3)pi r^(3)`
`implies (triangleV)/(V)=3xx(triangle r)/(r )`
Substituting from equation (i) we get the following :
`(triangleV)/(V)=(3)/(2)alpha`