Circles
Explore the key features of circles and learn to calculate circumference and area using pi (π).
Parts of a Circle
A circle is a set of all points that are the same distance from the centre. Understanding its key measurements is essential for calculating its size.
Radius (r)
The distance from the centre to the edge. All radii in a circle are equal.
Diameter (d)
The distance across a circle through the centre. d = 2r (twice the radius).
Circumference (C)
The perimeter (distance around) the circle.
Pi (π)
Pi (π) is the ratio of a circle's circumference to its diameter. No matter the size of the circle, this ratio is always the same special number.
π ≈ 3.14159...
An irrational number — its decimal places never end or repeat.
Use π ≈ 3.14 or the π button on your calculator.
Proof: Roll a circle of diameter 1 m along a straight line. The distance it travels in one full roll is π metres (approximately 3.14 m).
Circumference and Area Formulas
Circumference
C = πd or C = 2πr
Example: diameter = 10 cm
C = π × 10 = 31.4 cm
Area
A = πr²
Example: radius = 5 cm
A = π × 5² = π × 25 = 78.5 cm²
Key reminder: Circumference is measured in length units (cm, m). Area is measured in square units (cm², m²).
Other Circle Features
Chord
A straight line joining two points on the edge. The longest chord is the diameter.
Arc
A curved part of the circumference between two points on the circle.
Sector
A "pie slice" region bounded by two radii and an arc. Like a slice of pizza.
Key Vocabulary
Radius
The distance from the centre to the edge. Half the diameter.
Diameter
The distance across the circle through the centre. Twice the radius.
Circumference
The perimeter of a circle. Calculated using C = πd.
Pi (π)
A mathematical constant ≈ 3.14159. The ratio of circumference to diameter.
Worked Examples
A circle has a radius of 7 cm. Calculate its circumference. (Use π ≈ 3.14)
Formula: C = 2πr
C = 2 × 3.14 × 7
C = 6.28 × 7 = 43.96 cm
A circular swimming pool has a diameter of 8 m. Find its area. (Use π ≈ 3.14)
Step 1: radius = diameter ÷ 2 = 8 ÷ 2 = 4 m
Step 2: A = πr² = 3.14 × 4² = 3.14 × 16
Answer: 50.24 m²
A circular plate has a circumference of 62.8 cm. Find its radius. (Use π ≈ 3.14)
Formula: C = 2πr, so r = C ÷ (2π)
r = 62.8 ÷ (2 × 3.14) = 62.8 ÷ 6.28
Answer: r = 10 cm
Knowledge Check
Use π ≈ 3.14 unless told otherwise. Select the correct answer for each question.
Question 1
A circle has a diameter of 20 cm. What is its radius?
Question 2
Calculate the circumference of a circle with diameter 5 cm. (Use π ≈ 3.14)
Question 3
Calculate the area of a circle with radius 3 cm. (Use π ≈ 3.14)
Question 4
Which formula gives the circumference of a circle using the radius?
Question 5
A circle has a radius of 6 m. What is its diameter?
Key Concepts Summary
- ●The radius (r) is half the diameter (d): d = 2r.
- ●Pi (π) ≈ 3.14 is the fixed ratio of circumference to diameter in any circle.
- ●Circumference: C = πd or C = 2πr (measured in length units).
- ●Area: A = πr² (measured in square units).
- ●When given the diameter, always halve it to find the radius before calculating area.