Last reviewed: 10 November 2026
Updated November 2026. These Grade 8 circles notes cover the circumference of a circle, the length of an arc and the perimeter of a sector. Circumference = πd = 2πr. An arc is a fraction of the circumference: arc length = (θ ÷ 360) × 2πr, where θ is the angle at the centre. The perimeter of a sector is the arc length plus the two radii. Using π = 22/7, a circle of radius 7 cm has circumference 2 × 22/7 × 7 = 44 cm.
The examples and questions are original practice for Kenyan junior school learners, not an official paper. For the other Grade 8 maths topics, see our Grade 8 mathematics revision guide and the Grade 8 notes hub.
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What the Grade 8 Curriculum Covers
Circles is a sub-strand under Measurements in the Kenya Institute of Curriculum Development’s Grade 8 Mathematics design. Learners work out the circumference of a circle, the length of an arc and the perimeter of a sector in real-life situations. The design is listed on the KICD Grade Eight curriculum designs page. Area of a circle and sectors belongs to the Area sub-strand, so it is not the focus here.
Parts of a Circle
- Radius (r): from the centre to the edge.
- Diameter (d): across the circle through the centre; d = 2r.
- Circumference: the distance all the way round.
- Arc: part of the circumference.
- Sector: a “slice” bounded by two radii and an arc.
Circumference
For every circle, circumference ÷ diameter is the same number, π (about 3.142 or 22/7). So C = πd = 2πr. This is the formula used in OpenStax Prealgebra’s section on circles and irregular figures. Use 22/7 when the radius is a multiple of 7, and 3.142 otherwise, unless the question says which value to use.
Worked example: a bicycle wheel
A wheel has radius 35 cm. Circumference = 2 × 22/7 × 35 = 220 cm. In 100 complete turns the bicycle travels 100 × 220 = 22,000 cm = 220 m.
Worked example: finding the radius
A circular flower bed has circumference 88 m. Then 2 × 22/7 × r = 88, so r = 88 × 7 ÷ 44 = 14 m.
Length of an Arc
An arc with centre angle θ is θ/360 of the full circle, so arc length = (θ ÷ 360) × 2πr.
Worked example
Find the length of an arc subtending 60° at the centre of a circle of radius 21 cm.
- Fraction of the circle: 60 ÷ 360 = 1/6.
- Circumference: 2 × 22/7 × 21 = 132 cm.
- Arc length: 132 ÷ 6 = 22 cm.
A semicircle is the arc for θ = 180°, which is half the circumference.
Perimeter of a Sector
The boundary of a sector is the arc plus two radii: perimeter = arc length + 2r. Forgetting the two straight edges is the most common mistake.
Worked example
Using the 60° sector above: perimeter = 22 + 21 + 21 = 64 cm.
Worked example: a fan-shaped flower bed
A gardener edges a sector-shaped bed with radius 3.5 m and angle 90° (a quarter circle). Arc = (90 ÷ 360) × 2 × 22/7 × 3.5 = 5.5 m. Perimeter = 5.5 + 3.5 + 3.5 = 12.5 m of edging.
Worked example: a semicircular window frame
A window is a semicircle of diameter 1.4 m. The curved part is half of π × 1.4 = (22/7 × 1.4) ÷ 2 = 2.2 m. The straight base is 1.4 m, so the frame is 2.2 + 1.4 = 3.6 m long.
Original Practice Questions With Worked Answers
- Find the circumference of a circle of diameter 28 cm (π = 22/7). 22/7 × 28 = 88 cm.
- Find the arc length for 120° in a circle of radius 14 cm. (1/3) × 2 × 22/7 × 14 = 88/3 ≈ 29.3 cm.
- Find the perimeter of that sector. 29.3 + 28 ≈ 57.3 cm.
- A circular track has circumference 440 m. Find its radius. r = 440 × 7 ÷ 44 = 70 m.
- A wheel of radius 0.7 m turns 50 times. How far does it travel? 2 × 22/7 × 0.7 = 4.4 m per turn; 50 × 4.4 = 220 m.
Cover the answers and attempt each question first. For timed practice, use the Grade 8 revision papers or the Grade 8 CBC Challenge. These notes are free; full revision access is available with the KSh 20 Day Pass or the KSh 500 Monthly Pass.
Frequently Asked Questions
What is the formula for the circumference of a circle?
Circumference = πd or 2πr, where d is the diameter and r the radius.
How do you find the length of an arc?
Multiply the circumference by the fraction of the circle: (angle at the centre ÷ 360) × 2πr.
What is the perimeter of a sector?
The arc length plus the two radii.
Should I use 22/7 or 3.142 for π?
Use the value the question gives. If none is given, 22/7 is convenient when the radius is a multiple of 7.