What is the formula for the area of a sector?
Sectors: Arc Length and Area (Updated)

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Mathematics
•
8th - 10th Grade
•
Hard
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1.
FLASHCARD QUESTION
Front
Back
Area = (θ/360) × πr², where θ is the angle in degrees and r is the radius.
2.
FLASHCARD QUESTION
Front
How do you calculate the arc length of a sector?
Back
Arc Length = (θ/360) × 2πr, where θ is the angle in degrees and r is the radius.
3.
FLASHCARD QUESTION
Front
What does the term 'sector' refer to in geometry?
Back
A sector is a portion of a circle enclosed by two radii and the arc between them.
4.
FLASHCARD QUESTION
Front
If the radius of a sector is 5 m and the angle is 60 degrees, what is the area of the sector?
Back
Area = (60/360) × π(5)² = 13.09 m² (approximately).
5.
FLASHCARD QUESTION
Front
What is the relationship between the angle of a sector and its area?
Back
The area of a sector is directly proportional to the angle; larger angles yield larger areas.
6.
FLASHCARD QUESTION
Front
How do you convert radians to degrees for sector calculations?
Back
Degrees = Radians × (180/π).
7.
FLASHCARD QUESTION
Front
What is the area of a sector with a radius of 10 cm and an angle of 90 degrees?
Back
Area = (90/360) × π(10)² = 78.54 cm² (approximately).
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