Area of a Sector of a Circle

Area of a Sector of a Circle

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?

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?

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?