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The dimensions of a cube are measured with vernier callipers.

The measured length of each side is $30 \text{mm}$. If the vernier callipers can be read with an uncertainty of $\pm 0.1\text{mm}$, what does this give for the approximate uncertainty in the value of its volume?

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Since volume $V=t^3$, the fractional uncertainty in the value of volume is given by

$\dfrac{\Delta V}{V} = 3 \left(\dfrac{\Delta t}{t} \right) = \pm 3 \left(\dfrac{0.1}{30} \right) = \pm 0.01 = \pm 1\%$
by Diamond (75,918 points)

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