Answer to Question #242710 in Calculus for dev

Question

The volume of a sphere is to be computed from the measured value of its radius. Estimate the maximum permissible percentage error in the measurement if the percentage error in the volume must be kept within ±6%.

Answer 1

Let V be the volume of the sphere and r be its radius.

V = (4/3)π r ³

Δ ​V/V = (3(4/3) π r²)Δr/((4/3π r³)

= 3Δ r/r

Δ ​V/V = ±6%

Δ r/r = ±2%

 

Answer: Maximum permissible error in the measurement of

its radius is ± 2%