Find the area of a sector of a circle with radius 7 cm if the angle of the sector is 60°.
Answer: πr2 × θ360 = 227 × 49 × 60360 = 773 ≈ 25.67 cm2.
Step-by-step solution
Given: r = 7 cm; θ = 60°
To find: Area of the sector
To find: Area of the sector
Idea: A sector with angle θ° is θ360 of the whole disc.
- Area = πr2 × θ360° = 227 × 7 × 7 × 60°360°.1 mark
- = 154 × 16 = 773 ≈ 25.67 cm2.1 mark
Area of the sector = 77/3 cm² ≈ 25.67 cm².
Check: The whole circle is 154 cm2, and 60° is one-sixth of a turn: 154 ÷ 6 ≈ 25.67 ✓.
Answer to write in the exam
Area = πr2 × θ360° = 227 × 7 × 7 × 60°360°
= 154 × 16
∴ Area = 773 ≈ 25.67 cm2
Common mistakes that cost marks
- Using 2πr × θ360, which is the arc length, not the area.
- Using 60180 instead of 60360.
How this can come in the exam
MCQ (1 mark)
The area of a sector of radius 14 cm and angle 45° is (use π = 227)
- 38.5 cm2
- 154 cm2
- 11 cm2
- 77 cm2
Show answer
(D) 77 cm2
227 × 196 × 45360 = 616 × 18 = 77 cm2.
Try one yourself
Find the area of a sector of radius 21 cm with angle 40°. (Use π = 227.)
Show answer
227 × 441 × 40360 = 1386 × 19 = 154 cm2.
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