Circles: from slices to πr²
Cut a round roti-shaped circle into slices and lay them top to tail. With more slices they make a rectangle πr long and r tall, so the area is πr²; then see what doubling the radius does.
Core concept
Circumference = 2πr and area = πr²: a circle's slices rearrange into a rectangle πr by r
Topic: Area and perimeter
The distance round a circle is its circumference: C = 2πr, where r is the radius and π is about 3.14. To find the area: How much flat space a shape covers, measured in square units like cm². All key words, cut the circle into equal slices, like a roti, and lay them top to tail, one pointing up, the next pointing down. The more slices you cut, the more the row looks like a rectangle. Its height is the radius r, and its length is half the circumference, πr. So the area of the circle is πr × r = πr².
What you will learn
- Find the circumference of a circle using C = 2πr.
- Explain why the area of a circle is πr², by rearranging its slices.
- Show that doubling the radius makes the area four times as big.
Before you start
- Know the radius and diameter of a circle, and that π is about 3.14.
- Find the area of a rectangle.
Materials
- Paper circles, a pencil and a ruler
- Scissors
Equipment
- A pair of compasses
Procedure
- Draw a circle of radius 5 cm and find its circumference and area.
- Cut it into more and more slices and lay them top to tail.
- Double the radius and compare the area.
- Compare the circle's area with the square drawn round it.
How this simulation is simplified
- π is taken as 3.14159…; answers are rounded to one decimal place.