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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![### Problem Statement
A sector of a circle has a central angle of 120°. Find the area of the sector if the radius of the circle is 7 cm.
*Enter your answer in the provided input box.*
\[ \boxed{\phantom{answer}} \text{ cm}^2 \]
---
**Explanation:**
To find the area of the sector of a circle, you can use the formula:
\[ \text{Area of Sector} = \left( \frac{\theta}{360} \right) \times \pi r^2 \]
Where:
- \(\theta\) is the central angle in degrees.
- \(r\) is the radius of the circle.
Given:
- \( \theta = 120^\circ \)
- \( r = 7 \) cm
Plugging these values into the formula:
\[ \text{Area of Sector} = \left( \frac{120}{360} \right) \times \pi \times (7)^2 \]
Calculate the area to find the answer.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fb98bdb5b-53bd-47c2-bd74-197e9ff57506%2Fb65be361-bb4d-4e9c-8025-341ea1fff86b%2F6vne2ao_processed.png&w=3840&q=75)
Transcribed Image Text:### Problem Statement
A sector of a circle has a central angle of 120°. Find the area of the sector if the radius of the circle is 7 cm.
*Enter your answer in the provided input box.*
\[ \boxed{\phantom{answer}} \text{ cm}^2 \]
---
**Explanation:**
To find the area of the sector of a circle, you can use the formula:
\[ \text{Area of Sector} = \left( \frac{\theta}{360} \right) \times \pi r^2 \]
Where:
- \(\theta\) is the central angle in degrees.
- \(r\) is the radius of the circle.
Given:
- \( \theta = 120^\circ \)
- \( r = 7 \) cm
Plugging these values into the formula:
\[ \text{Area of Sector} = \left( \frac{120}{360} \right) \times \pi \times (7)^2 \]
Calculate the area to find the answer.
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