Arc Lengths and Sectors Worksheet

Arc Lengths and Sectors Worksheet

Read each question carefully and provide the best answer. Show all your work for full credit.

1. Find the length of arc AB in a circle with a radius of 8 cm and a central angle of 45 degrees. Round your answer to two decimal places.

2. Calculate the area of a sector in a circle with a radius of 12 meters and a central angle of 120 degrees. Round your answer to two decimal places.

3. The formula for the length of an arc (L) with radius (r) and central angle (θ in radians) is L =  .

4. The formula for the area of a sector (A) with radius (r) and central angle (θ in radians) is A =  .

5. A circle has a radius of 5 cm. What is the length of an arc subtended by a central angle of 2.5 radians?

6. Find the area of a sector with a radius of 10 inches and a central angle of π/3 radians.

7. An arc has a length of 15 cm in a circle with a radius of 6 cm. Find the central angle in radians.

8. If the central angle of a sector is doubled, its area will also be doubled, assuming the radius remains constant.