If the radius of a sphere is measured as 7 m with an error or 0.02 m, find the approximate error in calculating its volume.

Explanation

Let r be radius and V be the volume of sphere.
Given r = 7 m and ` Delta r = 0.2 m`
Volume of sphare `V=4/3 pi r^(3)`
` rArr (dV)/(dr) = 4 pi r^(2)`
`:. Dleta V = (dV)/(dr) * Dleta r = 4 pi r^(2) Delta r`
`rArr" approximate error in volume "= 4pi xx 7 xx 7 xx 0.2`
` = 3.92 pi m^(3) `.