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A metal sphere has a mass of (40.0 ± 0.4) g and a diameter of (2.20 ± 0.01) cm…

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A metal sphere has a mass of $(40.0 \pm 0.4)\ \text{g}$ and a diameter of $(2.20 \pm 0.01)\ \text{cm}$ . Find its volume, its density, and the percentage error in the density.

Need a reminder? The key ideaShow

For a sum or a difference, the absolute errors add. For a product or a quotient, the relative errors add, each multiplied by its power:

\displaystyle Z = \frac{A^p B^q}{C^r} \;\Rightarrow\; \frac{\Delta Z}{Z} = p\frac{\Delta A}{A} + q\frac{\Delta B}{B} + r\frac{\Delta C}{C}

For a sphere, $V = \dfrac{\pi d^3}{6}$ and $\rho = \dfrac{m}{V}$ .

The worked solution

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Work it out on paper first. It is fine to get stuck or make a mistake: that is how we learn. When you are ready, go through the solution one step at a time, and check each step against your own.

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