Arc Length & Sector Area Reteach

Arc Length & Sector Area

By Andrew Schmitt

Radius: Line segment from the center to the edge of the circle.  

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Diameter: Line segment from edge to edge, through the center of the circle.

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Circumference: Distance (length) around the perimeter of the circle.

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Area:​ The space contained by the edge of the shape.

Circle Vocab

Multiple Choice

The distance from the center of the circle to any point on the circle is called the...

• radius

• diameter

• area

• circumference

• arc length

Multiple Choice

If the radius of a circle is 8 cm, the diameter is...

• $$16\ cm$$  

• $$64\pi\ cm^2$$  

• $$16\pi\ cm$$  

• $$4\ cm$$  

• None of the above

Multiple Choice

Find the radius of a circle whose diameter is 40 ft.

• 40ft
• 80ft
• 20ft
• 45ft

Multiple Select

Select all segments that are a radius of Circle A.

• DA
• AH

• HI
• AI

• ED

Multiple Choice

Daniel wants to buy cookies for her friend. The diameter of a cookie is 10 inches. What is the cookie’s circumference?

• 10 in
• 2.5 in
• 15.7 in
• 31.4 in 

Multiple Choice

Ms. Catall is using a compass to find her way out of the woods. The compass has a radius of 4 centimeters. What is the compass's area?

• 49.2 cm²
• 45.6 cm²
• 50.24 cm²
• 55.9 cm²

Arc Measure: The degree measure of a given arc.

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Arc Length: The length around the circumference of a given arc.

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Sector Area: The area of a given section of the circle.

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Circle Concepts

Multiple Choice

Find the length of the bold arc. Leave pi in your answer.

• 5688π ft
• 15.8π ft
• 150.4π ft
• 54,150 ft

Multiple Choice

Find the arc length of the bolded arc.

• A

• B

• C

• D

Multiple Choice

Find the arc length of the bolded arc. Give your answer in terms of π.

• (65/12)π cm

• 17.02 cm

• (845/24)π cm

• 26π cm

Multiple Choice

Alison is jogging on a circular track that has a radius of 140 feet.  She runs along the track from point R to point N, a distance of 230 feet. Find to the nearest degree, the measure of minor arc RN.

• 47
• 74
• 94
• 123

Multiple Choice

Find the area of the shaded sector of circle O. The radius is 6 inches and the central angle is 100°. Express answer to the nearest tenth of a square inch.

• 25.2 in²

• 28.5 in²

• 31.4 in²

• 38.2 in²

Multiple Choice

What is the area of the shaded SECTOR? Round to the nearest hundredth.

• 9.42 u²

• 113.10 u²

• 284.3 u²

• 452.39 u²

Multiple Choice

Stephanie is cutting a pie. Stephanie's mother wants one fourth of the pie. The diameter is 20 cm. What is the sector area of the pie her mother does not want?

• 235.62 cm squared
• three fourths of the pie
• 78.54 cm squared
• 83.99 cm squared

Multiple Choice

Find the exact area of the shaded space.
Think: What does exact mean?

• 36π units squared
• 144π/3 units squared
• 157.82 units squared
• 10. 92 units squared

Multiple Choice

A cathedral window is built in the shape of a semicircle. If the window is to contain three stained glass sections of equal size, what is the area of each stained glass section?  Express answer to the nearest square foot. HINT: How many degrees in a semicircle? What's the radius?

• 1 sq. ft
• 13 sq. ft
• 3 sq. ft
• 26 sq. ft