Circles · Grade 8
In Grade 8 you learn: arcs and sectors.
A circle is all the points the same distance (the radius) from its centre. The distance round it, the circumference, and the space inside, the area, both depend on the radius and on the special number π ≈ 3.14159.
Key facts
- Diameter = 2 × radius.
- Circumference C = πd = 2πr.
- Area A = πr² (square the radius, not the diameter).
- A chord joins two points on the circle; a tangent touches it at one point; an arc is part of the circumference.
- Leave answers “in terms of π” (like 25π) when asked for an exact answer.
Worked examples
Example 1
Find the circumference of a circle with diameter 9 cm, to 1 decimal place.
Answer: 28.3 cm
Example 2
A circular rug has a diameter of 3 m. Find its area, to 1 decimal place.
Answer: 7.1 m²
Example 3
A circle has a circumference of 50 cm. Find its area, to 1 decimal place.
Answer: 198.9 cm²