The volume $V = \pi r ^ { 2 } h$ of a right circular cylinder is to be calculated from measured values of r and h.Suppose r is measured with an error of no more than 2.5% and h with an error of no more than 1%.Using differentials, estimate the percentage error in the calculation of V.
(In general, in measuring a quantity Q, the percentage error is dQ/Q.)

Question

Quizplus · Accepted Answer

The Answer of The volume $V = \pi r ^ { 2 } h$ of a right circular cylinder is to be calculated from measured values of r and h.Suppose r is measured with an error of no more than 2.5% and h with an error of no more than 1%.Using differentials, estimate the percentage error in the calculation of V.
(In general, in measuring a quantity Q, the percentage error is dQ/Q.)

The Volume V=πr2hV = \pi r ^ { 2 } hV=πr2h

The Volume $V = \pi r ^ { 2 } h$