A cylindrical measuring cup has radius and height

PHYSICS · Multi-part · Fermi University Physics · Scientific Practice & Experimental Methods · Uncertainty in measurement · Uncertainty in measurement

Measurement and Method, Ch Propagating uncertainty into the quantity you actually want

Problem

A cylindrical measuring cup has radius

r = (2.50 \pm 0.03)\,\mathrm{cm}

and height

h = (8.00 \pm 0.05)\,\mathrm{cm}

, each uncertainty a standard deviation. The volume is

V = \pi r^2 h

. Treat

r

and

h

as independent. ((a)) Find the contribution of

r

V

by recomputing

V

with

r

moved up to

r + u(r)

, keeping

h

fixed; do the same for

h

. ((b)) Combine the two contributions to give

u(V)

, and quote

V = \bar V \pm u(V)

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