Percentage error in the measurement of h...

Percentage error in the measurement of height and radius of cylinder are x and y respectively. Find percentage error in the measurement of volume. Which of the two measurements height or radius need more attention?

Text Solution

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Height of cylinder = x
Radius of cylinder = y
Volume of cylinder = `pi y^(2) x`
Percentage error in volume
`(DeltaV)/(V) xx100 = pm (2(Deltay)/(y)+(Deltax)/(x))xx100`
Hence radius needs more attention because any error in its measurement is multiplied 2 time.

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