Arc Lengths and Sectors Worksheet

Arc Lengths and Sectors

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

1. What is the formula for the length of an arc of a circle with radius 'r' and central angle 'θ' in radians?

2. The area of a sector of a circle with radius 'r' and central angle 'θ' in degrees is given by:

1. The length of an arc is a portion of the   of the circle.

2. A sector of a circle is a region bounded by two   and an arc.

3. To convert degrees to radians, you multiply the degree measure by  .

1. Calculate the length of an arc in a circle with a radius of 10 cm and a central angle of 60 degrees. (Use π ≈ 3.14)

2. A circular pizza has a radius of 12 inches. If a slice (sector) of the pizza has a central angle of 45 degrees, what is the area of that slice? (Use π ≈ 3.14)

1. The arc length of a semicircle is half the circumference of the full circle.

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

1. A pendulum of length 50 cm swings through an angle of 0.5 radians. What is the length of the arc traced by the tip of the pendulum?

2. A circular garden has a radius of 8 meters. A sprinkler waters a sector of the garden with a central angle of 120 degrees. What is the area of the watered portion of the garden? (Use π ≈ 3.14)