ChapterP: Prerequisites
SectionP.6: The Rectangular Coordinate System And Graphs
Problem 37E: An airplane flies from Naples, Italy, in a straight line to Rome, Italy, which is 120 kilometers...
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![### Problem Statement
**Given:**
- \( P \) is the center of the circle.
- The area of the circle is \( 36\pi \) square feet.
**Task:**
- Find the area of the shaded sector.
- Leave your answer in terms of \( \pi \).
- Choose the correct units.
### Diagram Explanation
The diagram shows a circle with its center labeled as \( P \). A sector of the circle is shaded, and the angle subtended by this sector at the center is 100 degrees.
To solve this problem, you will use the formula for the area of a sector, which is given by:
\[ \text{Area of sector} = \left( \frac{\theta}{360} \right) \times \pi r^2 \]
where \( \theta \) is the central angle of the sector in degrees.
Given that the total area of the circle is \( 36\pi \) square feet, you should:
1. Determine the radius using \( A = \pi r^2 \).
2. Plug in the values into the sector area formula with \( \theta = 100^\circ \).
#### Answer Input
- Provide your answer in terms of \( \pi \).
- Choose the correct units (either \( \text{feet} \) or \( \text{feet}^2 \)).
### Interactive Section
Input your answer below:
\[ \text{Answer:} \]
(Interactive box for typing the answer)
Choose the correct units:
- [ ] feet
- [ ] feet²](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa49f6706-7e35-4891-ac6a-63de7331b23a%2F776ea757-1445-4bf8-982b-0ed7327720ff%2Fe6c4mgh_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Problem Statement
**Given:**
- \( P \) is the center of the circle.
- The area of the circle is \( 36\pi \) square feet.
**Task:**
- Find the area of the shaded sector.
- Leave your answer in terms of \( \pi \).
- Choose the correct units.
### Diagram Explanation
The diagram shows a circle with its center labeled as \( P \). A sector of the circle is shaded, and the angle subtended by this sector at the center is 100 degrees.
To solve this problem, you will use the formula for the area of a sector, which is given by:
\[ \text{Area of sector} = \left( \frac{\theta}{360} \right) \times \pi r^2 \]
where \( \theta \) is the central angle of the sector in degrees.
Given that the total area of the circle is \( 36\pi \) square feet, you should:
1. Determine the radius using \( A = \pi r^2 \).
2. Plug in the values into the sector area formula with \( \theta = 100^\circ \).
#### Answer Input
- Provide your answer in terms of \( \pi \).
- Choose the correct units (either \( \text{feet} \) or \( \text{feet}^2 \)).
### Interactive Section
Input your answer below:
\[ \text{Answer:} \]
(Interactive box for typing the answer)
Choose the correct units:
- [ ] feet
- [ ] feet²
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