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
Related questions
Question
![### Problem Statement
22. Find the area of the shaded region. Round your answer to the nearest tenth.
### Diagram Description
The image displays a circle with two internal segments shaded, forming a sector. The radius of the circle is labeled as 12.4 yards.
### Solution
To find the area of the shaded region in the circle:
1. **Area of the Entire Circle:**
The formula to find the area of a circle is:
\[
\text{Area} = \pi r^2
\]
where \( r \) is the radius of the circle.
Here, \( r = 12.4 \) yards.
\[
\text{Area} = \pi (12.4)^2 \approx 483.02 \text{ square yards}
\]
2. **Area of the Sector:**
To find the area of the shaded region, we need to know the angle of the sector, which is not provided in the problem statement. Without this information, we cannot proceed further. In a complete educational website setting, typically additional data such as the angle (in degrees or radians) of the sector should be provided to proceed with calculations.
### Conclusion
To accurately determine the area of the shaded region, the angle of the sector must be known. This step is crucial for further calculations involving the area of partial sections of the circle. Once the angle is given, the fractional area of the circle can then be calculated accordingly and the shaded region's area determined.
For now, based only on the given radius, the entire circle's area is approximately 483.0 square yards (rounded to the nearest tenth).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F8c8a549a-ce13-4c73-8e46-ff62e8d935c2%2F7757cb45-ce3b-44bc-9be7-28ce70ec992f%2Fduh4b3_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Problem Statement
22. Find the area of the shaded region. Round your answer to the nearest tenth.
### Diagram Description
The image displays a circle with two internal segments shaded, forming a sector. The radius of the circle is labeled as 12.4 yards.
### Solution
To find the area of the shaded region in the circle:
1. **Area of the Entire Circle:**
The formula to find the area of a circle is:
\[
\text{Area} = \pi r^2
\]
where \( r \) is the radius of the circle.
Here, \( r = 12.4 \) yards.
\[
\text{Area} = \pi (12.4)^2 \approx 483.02 \text{ square yards}
\]
2. **Area of the Sector:**
To find the area of the shaded region, we need to know the angle of the sector, which is not provided in the problem statement. Without this information, we cannot proceed further. In a complete educational website setting, typically additional data such as the angle (in degrees or radians) of the sector should be provided to proceed with calculations.
### Conclusion
To accurately determine the area of the shaded region, the angle of the sector must be known. This step is crucial for further calculations involving the area of partial sections of the circle. Once the angle is given, the fractional area of the circle can then be calculated accordingly and the shaded region's area determined.
For now, based only on the given radius, the entire circle's area is approximately 483.0 square yards (rounded to the nearest tenth).
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