Arcs and Sectors Worksheet
This worksheet focuses on understanding and calculating arc lengths and areas of sectors in circles, suitable for Grade 11 math students.
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Arcs and Sectors
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Read each question carefully and show all your work. Use π ≈ 3.14 where necessary. Round your answers to two decimal places unless otherwise specified.
1. An arc is a portion of the of a circle.
2. A sector is a region of a circle bounded by two radii and an .
3. The formula for the length of an arc is L = (θ/360°) * .
4. The formula for the area of a sector is A = (θ/360°) * .
1. A circle has a radius of 8 cm. Find the length of an arc subtended by a central angle of 45°.
2. The circumference of a circle is 30π meters. What is the length of an arc with a central angle of 120°?
1. Calculate the area of a sector with a radius of 10 inches and a central angle of 72°.
2. The area of a circle is 64π cm². Find the area of a sector with a central angle of 90°.
1. If the radius of a circle is 6 units and the arc length is 3π units, what is the central angle in degrees?
30°
60°
90°
120°
Refer to the diagram below. The radius of the circle is 5 cm and the central angle of the shaded sector is 100°.
1. Calculate the arc length of the shaded sector.
2. Calculate the area of the shaded sector.