In previous parts of this lesson, you developed a proportional relationship that can be used to calculate the area of the sector of a circle.

You can use this proportion to determine any of the three measures as long as you have information about the other two measures.

### Let’s solve a problem!

Photo courtesy of USDA Natural Resources Conservation Service, Source: NRCSCA06136 - California (1179)(NRCS Photo Gallery).tif, USDA NRCS, Wikimedia Commons

The Martinez family owns a farm in West Texas. They use a pivot irrigation system that waters crops from a central pivot point in a circle. The length of the irrigation pipe is 400 meters, and the family needs to grow at least 50,000 square meters of wheat. What is the smallest central angle that the pivot irrigation system will travel in order to meet this requirement?

• What information are you given?
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You know the length of the irrigation pipe (radius of the circle) is 400 meters and the area of the crop (area of the sector) is 50,000 square meters.
• What is the problem asking you to calculate?
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The problem is asking you to calculate the measure of the central angle.
• What other information do you need to calculate before you can use the proportion?
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You need to calculate the area of the circle before you can use the proportion.

Use the information presented in the problem to set up a proportion that you could solve in order to resolve the Martinez family’s problem. Click and drag the information from the dimensions box onto the appropriate place in the proportion. You may not use all of the information in the dimensions box.

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35.8°

Source: TTUMemorialCircle, Voltin, Wikimedia Commons

Memorial Circle at Texas Tech University is a memorial for all veterans that have attended Texas Tech University. At the center of the circle is Pfluger Fountain, and there are several sidewalks that cross the circle through its center, as shown in the diagram.

If the circumference of Memorial Circle is about 1,444 feet, what is the area of sector FCG?

• What information are you given?

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You know the circumference of the circle is about 1,444 feet and the measure of the central angle is 53°.

• What is the problem asking you to calculate?

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The problem is asking you to calculate the area of the sector.

• What other information do you need to calculate before you can use the proportion?

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You need to calculate the radius of the circle and the area of the circle before you can use the proportion.

Use the information presented in the problem to set up a proportion that you can solve in order to solve the problem. Click and drag the information from the dimensions box onto the appropriate place in the proportion. You may not use all of the information in the dimensions box.

• Solve the proportion. Express your answer to the nearest whole number.

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24,454 ft2

### Practice

Solve each problem below.

1. The area of the shaded sector is 169.56 square yards. What is the measure of the central angle used to create the sector?

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You need to calculate the area of the circle using the radius and then use the area of a sector proportion.

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2. A landscape designer is designing the landscaping for a circular park with a circumference of about 500 meters. She wants to plant a sector of the circular park using native grasses, and the sector should have an area of 750 square meters. What is the approximate measure of the central angle of the sector?

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Use the circumference to calculate the radius of the circular park, and then use the radius to calculate the area of the entire circular park. Determine the ratio of the area of the sector to the area of the entire park, and use that ratio to calculate the measure of the central angle of the sector.

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