Arc Lengths and Sectors Worksheet
This worksheet focuses on calculating arc lengths and areas of sectors in circles, suitable for Grade 12 Geometry students.
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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?