Answer to Question #241777 in Classical Mechanics for rao

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

$V =\frac{4}{3}\pi R^3$

$\epsilon(V)= \epsilon(\frac{4}{3})+\epsilon(\pi)+3*\epsilon(R)$

$|\epsilon(V)|<6\%$

$|\epsilon(\frac{4}{3})+\epsilon(\pi)+3*\epsilon(R)|<6\%$

$|3*\epsilon(R)|<6\%$

$\epsilon(R) ±2\%$

$\text{Answer: maximum permissible error in measuring }\newline \text{ the radius of the ball} ±2\%$