Question

The volume of a cylinder is calculated by multiplying the height by pi and the radius squared ( V = hπr2 ). If the percent uncertainty of the radius is 10% and the percent uncertainty of the height is 2%, what is the percent uncertainty of the volume?

Answer 1

Answer on Question #68598-Physics-Other

The volume of a cylinder is calculated by multiplying the height by pi and the radius squared ( $V = h\pi r^2$ ). If the percent uncertainty of the radius is $10\%$ and the percent uncertainty of the height is $2\%$ , what is the percent uncertainty of the volume?

Solution

The percent uncertainty of the area is

$$2 \frac {\Delta r}{r} = 2 (10 \%) = 20 \%$$

The percent uncertainty of the volume is

$$20\% = 2\% = 22\%.$$

Answer: $22\%$ .

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