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11. What is the area of the shaded area below? Answer in terms of r.,

11. What is the area of the shaded area below? Answer in terms of r.,

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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**Question:** 11. What is the area of the shaded area below? Answer in terms of π. **Diagram Description:** The diagram depicts a circle with a radius of 12 inches and a central angle of 60 degrees. One of the sectors of the circle is shaded. **Solution:** **Step 1:** Find the area of the entire circle. Formula for the area of a circle: \( \text{Area} = \pi \times \text{radius}^2 \) Given radius \( r = 12 \) inches, \( \text{Area}_{\text{circle}} = \pi \times (12)^2 \) \( \text{Area}_{\text{circle}} = 144\pi \) square inches **Step 2:** Find the area of the sector. The area of a sector of a circle is given by the formula: \( \text{Area}_{\text{sector}} = \left(\frac{\theta}{360}\right) \times \text{Area}_{\text{circle}} \) where \( \theta \) is the central angle of the sector in degrees. Given \( \theta = 60 \) degrees, \( \text{Area}_{\text{sector}} = \left(\frac{60}{360}\right) \times 144\pi \) \( \text{Area}_{\text{sector}} = \left(\frac{1}{6}\right) \times 144\pi \) \( \text{Area}_{\text{sector}} = 24\pi \) **Answer:** Area = 24π square inches
Transcribed Image Text:**Question:** 11. What is the area of the shaded area below? Answer in terms of π. **Diagram Description:** The diagram depicts a circle with a radius of 12 inches and a central angle of 60 degrees. One of the sectors of the circle is shaded. **Solution:** **Step 1:** Find the area of the entire circle. Formula for the area of a circle: \( \text{Area} = \pi \times \text{radius}^2 \) Given radius \( r = 12 \) inches, \( \text{Area}_{\text{circle}} = \pi \times (12)^2 \) \( \text{Area}_{\text{circle}} = 144\pi \) square inches **Step 2:** Find the area of the sector. The area of a sector of a circle is given by the formula: \( \text{Area}_{\text{sector}} = \left(\frac{\theta}{360}\right) \times \text{Area}_{\text{circle}} \) where \( \theta \) is the central angle of the sector in degrees. Given \( \theta = 60 \) degrees, \( \text{Area}_{\text{sector}} = \left(\frac{60}{360}\right) \times 144\pi \) \( \text{Area}_{\text{sector}} = \left(\frac{1}{6}\right) \times 144\pi \) \( \text{Area}_{\text{sector}} = 24\pi \) **Answer:** Area = 24π square inches
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