If you make a 1 percent error in the measurement of either the diameter or the length of a cylinder what is the error in the volume?

The volume ( V ) of a cylinder is calculated using the formula ( V = \pi r^2 h ), where ( r ) is the radius and ( h ) is the height. If there is a 1 percent error in either the diameter or the height, the resulting error in volume can be found using the formula for propagation of errors. A 1 percent error in the diameter (which affects the radius) leads to approximately a 2 percent error in volume, while a 1 percent error in height results in a 1 percent error in volume. Therefore, the maximum error in volume can be about 2 percent when considering the diameter measurement error.