Question

a certain cylinder has a length of 4cm and diameter 2cm.what percentage uncertainty is introduced into the calculated circumference by an uncertainty of 0.01cm in the diameter measurement?.what percent uncertainty does this introduce in the calculated volume?

Answer 1

$V=\frac{\pi d^2 l}{4},$

$\frac{\Delta d}{d}=\frac{0.01}{2}=0.005=0.5\%,$

$\frac{\Delta V}{V}=2\cdot \frac{\Delta d}{d}=1\%.$