Question: how to calculate percentage error in volume of sphere?
Answer: It depends on how precise you can measure the radius. The precision of the estimate of the radius will determine the precision of the volume. So the uncertainty is about 4/3π(3r ²Δr) = 4πr ²Δr if Δr is small compared to r. Divide by the volume 4/3πr³ to get the percent uncertainty = about 3Δr/r.