Last reviewed: 10 November 2026
Updated November 2026. These Grade 8 notes on the area of circles and sectors give the formulas and worked examples. The area of a circle is A = πr², where r is the radius. A sector is a slice of a circle, and its area is (θ/360) × πr², where θ is the angle at the centre in degrees.
The examples use π = 22/7 or 3.142 as stated. They are original practice, not an official paper. For circumference and arc length, see our Grade 8 circles notes, and for the other topics our Grade 8 mathematics revision guide.
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What the Grade 8 Curriculum Covers
Area is a sub-strand under Measurements in the Kenya Institute of Curriculum Development’s Grade 8 Mathematics design. It includes the area of circles, the area of a sector, surface area of solids, and the area of irregular shapes using square grids. The design is listed on the KICD Grade Eight curriculum designs page. Surface area is covered separately in our Grade 8 nets and surface area notes.
Area of a Circle
A = πr². Square the radius first, then multiply by π. If you are given the diameter, halve it to get the radius. The answer is in square units, such as cm² or m². The formula is explained in many open textbooks, including OpenStax Prealgebra 2e.
Example. Find the area of a circle of radius 7 cm (π = 22/7).
A = 22/7 × 7 × 7 = 22 × 7 = 154 cm².
Example. A round table top has a diameter of 1.2 m. Find its area (π = 3.142).
r = 0.6 m. A = 3.142 × 0.6 × 0.6 = 3.142 × 0.36 = 1.131 m² (to 3 decimal places).
Area of a Sector
A sector is the region between two radii and the arc joining them. Its area is the fraction θ/360 of the whole circle: A = (θ/360) × πr².
Example. Find the area of a sector with radius 14 cm and angle 90° (π = 22/7).
A = 90/360 × 22/7 × 14 × 14 = 1/4 × 616 = 154 cm².
Example. A sector of radius 21 cm has angle 60°. Area = 60/360 × 22/7 × 21 × 21 = 1/6 × 1,386 = 231 cm².
Working Backwards
If the area is given, divide by π and take the square root to find the radius. A circle has area 616 cm² (π = 22/7): r² = 616 × 7/22 = 196, so r = 14 cm.
Shaded Regions
Many questions ask for a shaded part. Find the whole area, then subtract the unshaded part. A square of side 14 cm has a circle of radius 7 cm drawn inside it touching all four sides. Shaded area outside the circle = 196 − 154 = 42 cm².
Original Practice Questions With Worked Answers
- Find the area of a circle of radius 3.5 cm (π = 22/7).
Answer: 22/7 × 3.5 × 3.5 = 38.5 cm². - A circular flower bed has a diameter of 28 m. Find its area (π = 22/7).
Answer: r = 14 m, A = 616 m². - Find the area of a sector of radius 7 cm and angle 120° (π = 22/7).
Answer: 120/360 × 154 = 51.33 cm² (to 2 decimal places). - A circle has area 154 cm² (π = 22/7). Find its radius.
Answer: r² = 154 × 7/22 = 49, so r = 7 cm. - A semicircle has radius 10 cm. Find its area (π = 3.142).
Answer: 1/2 × 3.142 × 100 = 157.1 cm².
For daily practice across subjects, a Day Pass (KSh 20) or Monthly Pass (KSh 500) opens the full question bank.
Frequently Asked Questions
What is the formula for the area of a circle?
A = πr², where r is the radius. If you know the diameter, halve it first.
How do I find the area of a sector?
Multiply the area of the whole circle by θ/360, where θ is the angle at the centre in degrees.
Should I use 22/7 or 3.142 for π?
Use whichever the question states. 22/7 is convenient when the radius is a multiple of 7.
What units is area measured in?
Area is measured in square units, such as cm², m² or km².
Ten-minute check: try the free Grade 8 CBC Challenge. It has 10 questions, each marked on the spot with the working, and it shows which topics to practise next.