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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![### Geometry Problem: Arc Length Calculation
**Problem Statement:**
The radius of a circle is 2 meters. What is the length of a 135° arc?
**Diagram Description:**
The diagram shows a circle with a radius of \( r = 2 \) meters. Within the circle, there is an arc highlighted in yellow, subtending a central angle of 135°.
**Calculation Steps:**
To find the length of an arc (\(s\)), you can use the formula:
\[ s = r \theta \]
where:
- \( r \) is the radius,
- \( \theta \) is the central angle in radians.
First, convert the angle from degrees to radians:
\[ 135° \times \frac{\pi}{180°} = \frac{3\pi}{4} \; \text{radians} \]
Now, apply the formula:
\[ s = 2 \times \frac{3\pi}{4} = \frac{3\pi}{2} \; \text{meters} \]
**Final Answer:**
\[ \frac{3\pi}{2} \; \text{meters} \]
**Fill in the Blank:**
\[ \boxed{\frac{3\pi}{2}} \; \text{meters} \]
Make sure to provide the exact answer in its simplest form.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F7f1c0988-ec46-4e74-b4f4-98be84cdb1c2%2Fd2eb9ccf-d683-4e6b-8a7d-f80851115746%2Fq7ss53l_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Geometry Problem: Arc Length Calculation
**Problem Statement:**
The radius of a circle is 2 meters. What is the length of a 135° arc?
**Diagram Description:**
The diagram shows a circle with a radius of \( r = 2 \) meters. Within the circle, there is an arc highlighted in yellow, subtending a central angle of 135°.
**Calculation Steps:**
To find the length of an arc (\(s\)), you can use the formula:
\[ s = r \theta \]
where:
- \( r \) is the radius,
- \( \theta \) is the central angle in radians.
First, convert the angle from degrees to radians:
\[ 135° \times \frac{\pi}{180°} = \frac{3\pi}{4} \; \text{radians} \]
Now, apply the formula:
\[ s = 2 \times \frac{3\pi}{4} = \frac{3\pi}{2} \; \text{meters} \]
**Final Answer:**
\[ \frac{3\pi}{2} \; \text{meters} \]
**Fill in the Blank:**
\[ \boxed{\frac{3\pi}{2}} \; \text{meters} \]
Make sure to provide the exact answer in its simplest form.
Transcribed Image Text:Below is a transcription of the multiple-choice options that might appear on an educational website:
---
### Question:
Select the correct value of the following expression:
#### Options:
- ⃝ \(3\pi\)
- ⃝ \(1.5\pi\)
- ⃝ \(6\pi\)
- ⃝ \(\pi\)
---
### Explanation:
The question presents four different multiple-choice answers using the mathematical constant \(\pi\) (pi). Each option has a circle next to it, which can be selected as an answer. The values provided are:
- \(3\pi\): Three times pi.
- \(1.5\pi\): One and a half times pi.
- \(6\pi\): Six times pi.
- \(\pi\): Pi itself.
This format is typically used in quizzes to assess the understanding of mathematical concepts involving \(\pi\).
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