If the radius of a sphere is measured as 7m with an error of 0.02m the

1.	If the radius of a sphere is measured as 7m with an error of 0.02m then find the approximate error in calculating its volume.
Answer» Let r be the radius of the sphere and ∆r be the error in measuring the radius then r =7m and ∆r = 0.02 m We have; V = \(\frac{4}{3}\) πr³ dV = \(\frac{dV}{dr}\) ∆r = \(\frac{4}{3}\) π3r² × ∆r = 4π(7)² × 0.02 = 3.92 π m³.

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

Answer»

Let r be the radius of the sphere and ∆r be the error in measuring the radius then r =7m and ∆r = 0.02 m

We have;

V = \(\frac{4}{3}\) πr³
dV = \(\frac{dV}{dr}\) ∆r = \(\frac{4}{3}\) π3r² × ∆r
= 4π(7)² × 0.02 = 3.92 π m³.