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A village in Kenya stores water in a spherical tank…

Try it on paper first. A hint, the key idea and the worked solution are here when you need them.

A village in Kenya stores water in a spherical tank. A surveyor measures its radius as $7.0\ \text{m}$ , with a possible error of $0.05\ \text{m}$ . Find the volume from the measured radius. Then use a differential to estimate the error in the volume, and the percentage error in the volume.

Need a reminder? The key ideaShow

$dy = f'(x)\,dx$ and $f(x + dx) \approx f(x) + f'(x)\,dx$ . The relative error is $\dfrac{dx}{x}$ , the percentage error is $\dfrac{dx}{x} \times 100\%$ , and for $y = x^n$ the relative error in $y$ is $n$ times that in $x$ .

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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