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,

Hence, the approximate error in calculating the volume is 3.92 π m³.