Circumference and area: the bicycle wheel
Unroll a wheel's rim along the road to discover π, cut the wheel into slices to find its area, and work out how far it rolls.
Core concept
The circumference of any circle is π × diameter, and its area is π × radius²
Topic: Circles
When a bicycle wheel turns once, it rolls forward exactly the length of its rim, the circumference. Laid flat, the rim is always a little more than 3 diameters long, for any wheel: rim ÷ diameter is the number π, about 3.14 (or 22/7). So C = π × d = 2πr. To find the area: How much flat space a shape covers, measured in square units like cm². All key words inside the wheel, cut it into equal slices and lay them head to tail: they make a shape close to a rectangle, half the rim (πr) long and one radius (r) high, so the area is πr × r = πr².
What you will learn
- Find π as the circumference divided by the diameter.
- Calculate the circumference and area of a circle.
- Solve a practical problem about the distance a wheel rolls.
Before you start
- Radius, diameter and the area of a rectangle.
Materials
- A bicycle wheel or a round plate, string and a paper circle
Equipment
- A measuring tape and scissors
Procedure
- Tap − or + to change the size of the wheel; read the rim laid flat in diameters.
- Tap the wheel to roll it more turns, and tap the slices to cut the wheel into more of them.
- Record three wheels of different sizes and compare rim ÷ diameter.
- Record how far the 35 cm wheel rolls in 10 turns, and cut a wheel into 32 slices.
How this simulation is simplified
- The wheel rolls without slipping; π is taken as 3.14159…