Arc Lengths and Sectors Worksheet
This worksheet focuses on calculating arc lengths and areas of sectors in circles, suitable for Grade 12 Geometry students.
Includes
Standards
Topics
Arc Lengths and Sectors
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Read each question carefully and show all your work. Round your answers to two decimal places where appropriate.
1. What is the formula for the length of an arc?
A = (θ/360) * πr²
L = (θ/360) * 2πr
A = πr²
L = 2πr
2. A circle has a radius of 10 cm. What is the area of a sector with a central angle of 90 degrees?
25π cm²
50π cm²
75π cm²
100π cm²
3. The portion of the circumference of a circle is called an .
4. A is a region of a circle bounded by two radii and an arc.
5. A circular garden has a radius of 8 meters. A sprinkler waters a sector of the garden with a central angle of 120 degrees. Calculate the area of the watered sector.
6. Find the length of an arc in a circle with a radius of 15 inches and a central angle of 60 degrees. Express your answer in terms of π.
7. The arc length of a semicircle is half the circumference of the circle.
True
False
8. If the central angle of a sector is doubled, the area of the sector is also doubled.
True
False
9. A circular pizza has a diameter of 16 inches. If the pizza is cut into 8 equal slices, what is the arc length of the crust of one slice?
10. An architect is designing a circular stained-glass window with a radius of 2 feet. A specific section of the window is a sector with an area of 3π square feet. What is the central angle of this sector in degrees?
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