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
![### Find the Area of the Shaded Sector
This problem involves calculating the area of a shaded sector within a circle.
#### Diagram Explanation:
- The diagram is of a circle centered at point O.
- The radius of the circle is labeled as 10 units.
- An angle of 18 degrees is formed at the center, corresponding to the shaded sector.
#### Steps to Calculate the Area of the Shaded Sector:
1. **Understand the formula**:
The area \( A \) of a sector of a circle can be determined using the following formula:
\[
A = \frac{\theta}{360} \times \pi r^2
\]
where:
- \(\theta\) is the central angle in degrees.
- \(r\) is the radius of the circle.
2. **Substitute the values**:
Here, \(\theta = 18^\circ\) and \(r = 10\).
So, we substitute these values into the formula:
\[
A = \frac{18}{360} \times \pi \times 10^2
\]
3. **Simplify the fractions**:
\[
A = \frac{1}{20} \times \pi \times 100
\]
4. **Calculate the area**:
\[
A = 5\pi
\]
Hence, the area of the shaded sector is \( 5\pi \) square units.
#### Final Answer
The area of the shaded sector is \( 5\pi \) square units.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F234dd4ba-addc-435e-a54f-15f12e8dfa5c%2Ff63f1e60-1fe3-4c63-b371-65da49d6dfb8%2Fndyqq6j_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Find the Area of the Shaded Sector
This problem involves calculating the area of a shaded sector within a circle.
#### Diagram Explanation:
- The diagram is of a circle centered at point O.
- The radius of the circle is labeled as 10 units.
- An angle of 18 degrees is formed at the center, corresponding to the shaded sector.
#### Steps to Calculate the Area of the Shaded Sector:
1. **Understand the formula**:
The area \( A \) of a sector of a circle can be determined using the following formula:
\[
A = \frac{\theta}{360} \times \pi r^2
\]
where:
- \(\theta\) is the central angle in degrees.
- \(r\) is the radius of the circle.
2. **Substitute the values**:
Here, \(\theta = 18^\circ\) and \(r = 10\).
So, we substitute these values into the formula:
\[
A = \frac{18}{360} \times \pi \times 10^2
\]
3. **Simplify the fractions**:
\[
A = \frac{1}{20} \times \pi \times 100
\]
4. **Calculate the area**:
\[
A = 5\pi
\]
Hence, the area of the shaded sector is \( 5\pi \) square units.
#### Final Answer
The area of the shaded sector is \( 5\pi \) square units.
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 2 steps with 2 images
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, geometry and related others by exploring similar questions and additional content below.Recommended textbooks for you
Elementary Geometry For College Students, 7e
Geometry
ISBN:
9781337614085
Author:
Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:
Cengage,
Elementary Geometry for College Students
Geometry
ISBN:
9781285195698
Author:
Daniel C. Alexander, Geralyn M. Koeberlein
Publisher:
Cengage Learning
Elementary Geometry For College Students, 7e
Geometry
ISBN:
9781337614085
Author:
Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:
Cengage,
Elementary Geometry for College Students
Geometry
ISBN:
9781285195698
Author:
Daniel C. Alexander, Geralyn M. Koeberlein
Publisher:
Cengage Learning