• Find the arc length labeled 's" given central angle is ST radians and radius is 9 in. Round to nearest tenth inch 9 in Ans. 23.6 inches • Find the area of the sector enclosed by arc "s" given central angle is radians and radius is 9 in. Round to nearest sq. in. Ans. 106 in² 9 in
• Find the arc length labeled 's" given central angle is ST radians and radius is 9 in. Round to nearest tenth inch 9 in Ans. 23.6 inches • Find the area of the sector enclosed by arc "s" given central angle is radians and radius is 9 in. Round to nearest sq. in. Ans. 106 in² 9 in
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
100%
![### Arc Length and Sector Area in Circles
**Problem 1: Find the Arc Length**
- **Given**: Central angle is \(\frac{5\pi}{6}\) radians and radius is 9 inches.
- **Formula**: Arc length \(s = r \theta\), where \(r\) is the radius and \(\theta\) is the central angle in radians.
- **Calculation**:
\[
s = 9 \times \frac{5\pi}{6} \approx 23.56 \text{ inches}
\]
- **Answer**: The arc length \(s\) is approximately 23.6 inches.
(Graph/Diagram: A circle with central angle \(\frac{5\pi}{6}\) radians and radius of 9 inches. The arc length \(s\) is highlighted.)
**Problem 2: Find the Area of the Sector**
- **Given**: Central angle is \(\frac{5\pi}{6}\) radians and radius is 9 inches.
- **Formula**: Area of the sector \(A = \frac{1}{2} r^2 \theta\).
- **Calculation**:
\[
A = \frac{1}{2} \times 9^2 \times \frac{5\pi}{6} \approx 106.06 \text{ square inches}
\]
- **Answer**: The area of the sector is approximately 106 square inches.
(Graph/Diagram: A circle with a sector defined by a central angle \(\frac{5\pi}{6}\) radians and radius 9 inches. The sector area is shaded.)
**Visual Explanation**:
- **First Diagram**: Illustrates a circle with radius 9 inches and an arc labeled \(s\) subtended by the angle \(\frac{5\pi}{6}\).
- **Second Diagram**: Shows the same circle, with the area of the sector enclosed by the arc \(s\) shaded.
### Summary:
These problems involve applying formulas for the arc length and sector area in circles, using specific given values for the radius and central angle in radians. Accurate calculations lead to the arc length and sector area, rounded to the nearest tenth of an inch and nearest square inch, respectively.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F66ae25c8-0515-4b9c-b99a-f65507bb17d7%2Fcf018c65-6f67-4678-8c42-81f21d875e19%2Fo44gmos_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Arc Length and Sector Area in Circles
**Problem 1: Find the Arc Length**
- **Given**: Central angle is \(\frac{5\pi}{6}\) radians and radius is 9 inches.
- **Formula**: Arc length \(s = r \theta\), where \(r\) is the radius and \(\theta\) is the central angle in radians.
- **Calculation**:
\[
s = 9 \times \frac{5\pi}{6} \approx 23.56 \text{ inches}
\]
- **Answer**: The arc length \(s\) is approximately 23.6 inches.
(Graph/Diagram: A circle with central angle \(\frac{5\pi}{6}\) radians and radius of 9 inches. The arc length \(s\) is highlighted.)
**Problem 2: Find the Area of the Sector**
- **Given**: Central angle is \(\frac{5\pi}{6}\) radians and radius is 9 inches.
- **Formula**: Area of the sector \(A = \frac{1}{2} r^2 \theta\).
- **Calculation**:
\[
A = \frac{1}{2} \times 9^2 \times \frac{5\pi}{6} \approx 106.06 \text{ square inches}
\]
- **Answer**: The area of the sector is approximately 106 square inches.
(Graph/Diagram: A circle with a sector defined by a central angle \(\frac{5\pi}{6}\) radians and radius 9 inches. The sector area is shaded.)
**Visual Explanation**:
- **First Diagram**: Illustrates a circle with radius 9 inches and an arc labeled \(s\) subtended by the angle \(\frac{5\pi}{6}\).
- **Second Diagram**: Shows the same circle, with the area of the sector enclosed by the arc \(s\) shaded.
### Summary:
These problems involve applying formulas for the arc length and sector area in circles, using specific given values for the radius and central angle in radians. Accurate calculations lead to the arc length and sector area, rounded to the nearest tenth of an inch and nearest square inch, respectively.
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 3 steps with 1 images
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