Question

A group of students is determining the density of a cube of metal. Using a calipers, they measure all three sides of the cube to be 2.000+ .002 cm . What is the volume they calculate, including the uncertainty?

Answer 1

The length of the side of the cube is

$a=(2.000\pm0.002)\ cm$

The volume of the cube is

$V=a^3=2.000^3=8\ cm^3$

And the uncertainty in the calculation of the volume can be given by

$\frac{u(V)}{V}=\frac{3u(a)}{a}$

$\Rightarrow u(V)=\frac{3V}{a}u(a)=\frac{3\times 8}{2}\times 0.002=0.024\ cm^3$

So, the volume of the cube with the uncertainty is

$V=\left (8.000\pm0.024 \right )\ cm^3$