What it shows
Rolling a round lid exactly one turn along a ruler marks out its circumference. For every lid, from a bottle cap to a steel plate, dividing the distance rolled by the diameter gives the same number, about 3.14, which is pi.
The science
The circumference of any circle is pi times its diameter, so the ratio is the same for a tiny cap and a huge wheel. Rolling turns the curved length into a straight one that a ruler can measure. Thread round the rim gives a second measurement. Both methods carry small errors in reading the marks, so the results cluster round 3.14 rather than hitting it exactly, and the larger objects give the closest values because the same reading error is a smaller share of a longer distance.
Materials
Cost: free. Many items come from home or from waste; spare parts such as LEDs, motors and wire are in the store.
- Five round objects: a bottle cap, a tin lid, a bangle, a steel plate and a bucket lid
- A long ruler or measuring tape
- A marker to mark the start point on each rim
- A sheet of paper and a calculator
- A thread for a second check
Safety
This project uses safe, everyday materials. Still, read the rules below with a parent before you start.
Never use mains electricity: power models with cells, batteries or a low-voltage adapter. Sharp and hot tools, flames and lab chemicals need an adult or your teacher beside you. Keep magnets, button cells and small parts away from young children, and wash your hands after making.
All the safety rulesStep by step
7 steps. Do them in order, and test each part before you go on to the next. Write what you notice in a notebook as you go.
Make a mark on the rim of each object and measure its diameter across the widest part with the ruler.
Place the mark on the zero of the ruler and roll the object in a straight line without slipping until the mark touches the ruler again.
Record the distance rolled as the circumference. Roll three times and average, since slipping is the main error.
Wrap thread once round the rim, mark it, and measure the thread as a second circumference.
Divide each circumference by its diameter and write the ratio in a table.
Plot circumference against diameter on graph paper; the points lie on a straight line through the origin with slope about 3.14.
Write a conclusion comparing your average ratio with 3.1416 and explaining which object gave the best result and why.
What you should see
All five objects give ratios between about 3.0 and 3.3 and the graph is a straight line through the origin, showing circumference is proportional to diameter with constant pi.
Viva questions
A teacher or a judge will ask how it works. Try to answer each question before you open it, then compare.
1What is pi?
The ratio of the circumference of any circle to its diameter, about 3.14159.
2A lid with diameter 7 cm rolls how far in one turn?
About 22 cm, since 22 divided by 7 is close to pi.
3Why did the biggest lid give the best answer?
A reading error of a few millimetres is a smaller fraction of a long distance than of a short one.
4Why does the graph pass through the origin?
A circle of zero diameter has zero circumference, and circumference is directly proportional to diameter.
Take it further
Measure the diameter of a bicycle wheel, count turns over 50 metres and check the distance with the formula.
Change one thing, measure what happens, and add a table or chart of your readings: that is what turns a model into your own investigation.
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