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? 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.

• Solve the proportion. Express your answer to the nearest tenth.

Interactive popup. Assistance may be required. 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? 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.

Interactive popup. Assistance may be required.

### 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? Interactive popup. Assistance may be required.

You need to calculate the area of the circle using the radius and then use the area of a sector proportion. Interactive popup. Assistance may be required.  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?

Interactive popup. Assistance may be required.

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. Interactive popup. Assistance may be required.  