Question

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

Answer 1

Let r be the radius of the sphere and ∆r be the error in measuring the radius. Then, r = 7 m and ∆r = 0.02 m Now, the volume V of the sphere is given by,

v=$\frac{4}{3}$πr3

\Rightarrow$$\frac{dv}{dr}=4πr2

$\Rightarrow$ dv=($\frac{dv}{dr}$)∇r

=(4πr2)∇r

4π(7)2(0.02)m3=3.92πm3

Hence, the approximate error in calculating the volume is 3.92 πm3.