Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Question
![**Problem Statement:**
Find the arc length. Round to two decimal places.
**Diagram Explanation:**
The diagram shows a circle with a highlighted sector. The radius (\(r\)) of the circle is 3 inches, and the central angle of the sector is 110 degrees.
**Steps to Solve:**
1. **Formula for Arc Length:**
\[
\text{Arc Length} = \frac{\theta}{360} \times 2\pi r
\]
where \(\theta\) is the central angle in degrees, and \(r\) is the radius of the circle.
2. **Substitute the Values:**
- \(\theta = 110\) degrees
- \(r = 3\) inches
3. **Calculate the Arc Length:**
\[
\text{Arc Length} = \frac{110}{360} \times 2\pi \times 3
\]
4. **Result (rounded to two decimal places):**
Calculate using a calculator for precision.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F0ecd4a66-8a79-4255-8635-c33dc6734dad%2Fc9959369-26f5-4c6d-8768-2dc2381a6c89%2Ftibo0zt_processed.png&w=3840&q=75)
Transcribed Image Text:**Problem Statement:**
Find the arc length. Round to two decimal places.
**Diagram Explanation:**
The diagram shows a circle with a highlighted sector. The radius (\(r\)) of the circle is 3 inches, and the central angle of the sector is 110 degrees.
**Steps to Solve:**
1. **Formula for Arc Length:**
\[
\text{Arc Length} = \frac{\theta}{360} \times 2\pi r
\]
where \(\theta\) is the central angle in degrees, and \(r\) is the radius of the circle.
2. **Substitute the Values:**
- \(\theta = 110\) degrees
- \(r = 3\) inches
3. **Calculate the Arc Length:**
\[
\text{Arc Length} = \frac{110}{360} \times 2\pi \times 3
\]
4. **Result (rounded to two decimal places):**
Calculate using a calculator for precision.
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