Area of a Sector of a Circle
Calculate the area of sectors of circles given radius and central angle, and solve related problems.
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Area of a Sector of a Circle
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Read each question carefully and provide your answer in the space provided. Show all your work for full credit. Remember the formula for the area of a sector: A = (θ/360°) * πr², where θ is the central angle in degrees and r is the radius.
1. Find the area of the sector of a circle with a radius of 8 cm and a central angle of 90°.
2. A circle has a radius of 12 inches. What is the area of a sector with a central angle of 60°? (Use π ≈ 3.14)
3. The area of a sector is a fraction of the total area of the .
4. If the central angle of a sector is 180°, the sector is a .
5. To find the area of a sector, you need the radius of the circle and the angle.
6. A sector has an area of 20π cm² and a central angle of 72°. What is the radius of the circle?
5 cm
10 cm
25 cm
50 cm
7. If the area of a circle is 100π units² and a sector of this circle has a central angle of 45°, what is the area of the sector?
12.5π units²
25π units²
50π units²
100π units²
8. A circular pizza has a diameter of 16 inches. If the pizza is cut into 8 equal slices, what is the area of one slice?
9. A lawn sprinkler sprays water in a circular pattern with a radius of 15 feet. If the sprinkler rotates 120°, what is the area of the lawn that gets watered?