A slice is a fraction of the pizza
A sector of angle θ is θ/360 of the circle, so its area is θ/360 × πr².
A 120° slice
A round pizza has radius 21 cm, so its area is πr² = 1386 cm² (taking π = 227). A slice is cut with an angle of 120° at the centre.
What is the area of the slice?
What this lesson covers
The idea
Area of a sector of angle θ (in degrees) of a circle of radius r = θ/360 × πr², obtained by the unitary method from the area πr² of the whole circle, a sector of 360°.
A 120° slice
A round pizza has radius 21 cm, so its area is πr² = 1386 cm² (taking π = 22/7). A slice is cut with an angle of 120° at the centre.
What is the area of the slice?
- 120 cm²
- 462 cm²
- 1266 cm²
Cut slices of a given area
Turn B round, or use the dial. The bar shows how much of the whole circle the slice takes. The working below shows the area, step by step.
The unitary method
Area of a sector = θ/360 × πr², where θ is the angle of the sector in degrees.
The whole circle is a sector of 360°, and its area is πr². So 1° gets πr² / 360, and θ° gets θ times that: θ/360 × πr².
For the pizza: 1° gets 1386 / 360 = 3.85 cm², so a slice of 120° has 120 × 3.85 = 462 cm². That is 120/360 = 1/3 of the whole circle.
Notes
Area of a sector = θ/360 × πr², found by the unitary method from the area πr² of the whole circle (360°).
Check yourself
The radius of a circle is 4 cm and the angle of a sector is 30°. Find the area of the sector. (Take π = 3.14)
Answer: 4.19 cm²
Area = 30/360 × 3.14 × 4 × 4 = 50.24 / 12 = 4.19 cm² (to two decimals).
A sector has angle 90° and radius 14 cm. Find its area. (Take π = 22/7)
Answer: 154 cm²
Area = 90/360 × 22/7 × 14 × 14 = 616 / 4 = 154 cm².
A sector of a circle of radius 21 cm has an area of 231 cm². Find the angle of the sector. (Take π = 22/7)
Answer: 60 °
231 / 1386 = 1/6, so the angle is 1/6 of 360° = 60°. Check: 60/360 × 1386 = 231.
The radius of a circle is doubled and the angle of its sector stays the same. What happens to the area of the sector?
- It becomes twice as big.. The area has r², not r. Doubling r makes r² four times as big.
- It becomes 4 times as big. — correct. Yes! The area is θ/360 × πr². With 2r in place of r, we get (2r)² = 4r².
- It stays the same.. A bigger radius makes a bigger circle, so the same angle takes a bigger slice.