The error in the measurement of the radius of a sphere is `0.5 %`. What is the permissible percentage error in the measurement of its (a) surface area and (b) volume ?

Answer

(a). `% ; (b) 1.5%`

Explanation

Given `Delta r // r = 0.5%`.
(a). The surface area of a sphere of radius `r is A = 4 pi r^(2)`.
Percentage error in `A = (Delta A)/(A) = ( 2 Delta r )/( r ) = 2 xx 0.5% = 1%`
(b). The volume of a sphere of radius `r is V = ( 4 pi)/(3) r^(3)`.
Percentage error in `V = ( Delta V) /( V) = ( 3 Delta r)/( r ) = 3 xx 0.5 % = 1.5%`