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23. What is the area of the figure to the nearest tenth? 165⁰° 3 in Work: Area = I in 2

23. What is the area of the figure to the nearest tenth? 165⁰° 3 in Work: Area = I in 2

Elementary Geometry For College Students, 7e
Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
ChapterP: Preliminary Concepts
SectionP.CT: Test
Problem 1CT
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### Problem 23 #### Question: What is the area of the figure to the nearest tenth? #### Given Information: - The figure is a sector of a circle with a central angle of 165 degrees - The radius of the circle is 3 inches #### Diagram: The provided diagram depicts a sector of a circle with a central angle labeled as 165 degrees and a radius of 3 inches. #### Work: *(Space provided for calculations)* #### Calculate Area: Area = ______ in² --- **Explanation of Graph/Diagram:** The diagram is a sector of a circle, which is a portion of the circle enclosed by two radii and the corresponding arc. The central angle of the sector is labeled as 165 degrees, and the length of the radius is given as 3 inches. To find the area of a sector of a circle, the formula is: \[ \text{Area} = \left( \frac{\theta}{360} \right) \times \pi r^2 \] where \(\theta\) is the central angle in degrees and \(r\) is the radius of the circle. Substituting the given values: \[ \theta = 165^\circ \] \[ r = 3 \, \text{inches} \] ### Try solving it on your own and then click "check answer" to verify your solution!
Transcribed Image Text:### Problem 23 #### Question: What is the area of the figure to the nearest tenth? #### Given Information: - The figure is a sector of a circle with a central angle of 165 degrees - The radius of the circle is 3 inches #### Diagram: The provided diagram depicts a sector of a circle with a central angle labeled as 165 degrees and a radius of 3 inches. #### Work: *(Space provided for calculations)* #### Calculate Area: Area = ______ in² --- **Explanation of Graph/Diagram:** The diagram is a sector of a circle, which is a portion of the circle enclosed by two radii and the corresponding arc. The central angle of the sector is labeled as 165 degrees, and the length of the radius is given as 3 inches. To find the area of a sector of a circle, the formula is: \[ \text{Area} = \left( \frac{\theta}{360} \right) \times \pi r^2 \] where \(\theta\) is the central angle in degrees and \(r\) is the radius of the circle. Substituting the given values: \[ \theta = 165^\circ \] \[ r = 3 \, \text{inches} \] ### Try solving it on your own and then click "check answer" to verify your solution!
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