Question

The diameter of a cylinder is(1.6±0.01)cm and its length is (5.0±0.1)cm . Calculate percentage error in its volume.

Answer 1

Answer:

For a "non-calculus" solution:

L = 5,   l = .1, D = 1.6, d = .01, v = error in volume

V = pi * (D/2)^2 * L = 10 cm^3

V + v = pi/4  (D + d)^2 * (L + l)

= pi/4 * (D^2 + 2 D d) * (L + l)      omit d^2 as it is small

= pi/4 ( L D^2 + 2 D d L  + l D^2)  omit 2 D L l d   as it is small

(V + v ) - V = pi/4 (2 D d L  + l D^2) = pi/4 * (.16  +  .256) = .327

Uncertainty in volume = .327

Using calculus

V = pi / 4 * D^2 L

dV = pi / 4 (2 D L dD + D^2 * dL)

dV = pi/4 ( 2 * 1.6 * 5 * .01 + 1.6^2 * .1) = .327

Since V = 10

The fractional error is .327 / 10 = .033 and

the percentage error is 3.3%