Quick answer: A sector with central angle θ in degrees and radius r has area (θ/360°)πr². It occupies the same fraction of the circle's area as its angle occupies of a full turn.
Worked example
Find the area of a 90° sector of radius 8 cm.
- The angle fraction is 90/360 = 1/4.
- The full circle area is π(8²) = 64π cm².
- Sector area = (1/4)64π = 16π cm².
Check the result
A 90° sector is one quarter of a circle, matching the result.
Stuck on a question? Ask it here and get a step-by-step answer in seconds — pay only per answer, no subscription. Ask your doubt now →
Common mistake to avoid
This is a sector, bounded by two radii and an arc. A circular segment is different and may require subtracting a triangle. For radians, use area = r²θ/2.
Try it yourself
1. Find a 60° sector area for radius 6 cm. 2. What is the area of a semicircle of radius 3 cm?
Answers and reasoning
1. (60/360)π36 = 6π cm². 2. (1/2)π9 = 9π/2 cm².
Need help with your own attempt? Ask a study question. AI answers require an account and paid credits. Check important steps with your textbook or teacher.
Stuck on a question? Ask it here and get a step-by-step answer in seconds — pay only per answer, no subscription. Ask your doubt now →