Find the area of a sector with a central angle of 160° and a dlameter of 8.6 cm. Round to the nearest tenth. O 7.6 cm2 O 25.8 cm2 O 103.3 cm2 O 3 cm?
Find the area of a sector with a central angle of 160° and a dlameter of 8.6 cm. Round to the nearest tenth. O 7.6 cm2 O 25.8 cm2 O 103.3 cm2 O 3 cm?
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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![**Question:**
Find the area of a sector with a central angle of 160° and a diameter of 8.6 cm. Round to the nearest tenth.
**Options:**
- ○ 7.6 cm²
- ○ 25.8 cm²
- ○ 103.3 cm²
- ○ 3 cm²
**Explanation:**
To find the area of a sector, you can use the formula:
\[ \text{Area of sector} = \left( \frac{\theta}{360} \right) \times \pi \times r^2 \]
Where:
- \(\theta\) is the central angle in degrees
- \(r\) is the radius of the circle
Given:
- Central angle (\(\theta\)) = 160°
- Diameter = 8.6 cm
First, calculate the radius \(r\):
\[ r = \frac{\text{diameter}}{2} = \frac{8.6}{2} = 4.3 \text{ cm} \]
Then plug these values into the formula:
\[ \text{Area of sector} = \left( \frac{160}{360} \right) \times \pi \times (4.3)^2 \]
Simplify the fraction:
\[ \left( \frac{160}{360} \right) = \left( \frac{4}{9} \right) \]
Now calculate:
\[ \text{Area of sector} = \left(\frac{4}{9}\right) \times \pi \times 18.49 \]
\[ \text{Area of sector} \approx \left(\frac{4}{9}\right) \times 3.1416 \times 18.49 \]
\[ \text{Area of sector} \approx \left(\frac{4}{9}\right) \times 58.09 \]
\[ \text{Area of sector} \approx 25.827 \text{ cm}^2 \]
Rounded to the nearest tenth:
\[ \text{Area of sector} \approx 25.8 \text{ cm}^2 \]
Therefore, the correct option is:
- ○ 25.8 cm²](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fe59874f9-f705-461a-94a3-07d771601ab4%2Ff707d2bb-b3f9-4c8b-8cd0-8086833ec528%2Fc0x0qks_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Question:**
Find the area of a sector with a central angle of 160° and a diameter of 8.6 cm. Round to the nearest tenth.
**Options:**
- ○ 7.6 cm²
- ○ 25.8 cm²
- ○ 103.3 cm²
- ○ 3 cm²
**Explanation:**
To find the area of a sector, you can use the formula:
\[ \text{Area of sector} = \left( \frac{\theta}{360} \right) \times \pi \times r^2 \]
Where:
- \(\theta\) is the central angle in degrees
- \(r\) is the radius of the circle
Given:
- Central angle (\(\theta\)) = 160°
- Diameter = 8.6 cm
First, calculate the radius \(r\):
\[ r = \frac{\text{diameter}}{2} = \frac{8.6}{2} = 4.3 \text{ cm} \]
Then plug these values into the formula:
\[ \text{Area of sector} = \left( \frac{160}{360} \right) \times \pi \times (4.3)^2 \]
Simplify the fraction:
\[ \left( \frac{160}{360} \right) = \left( \frac{4}{9} \right) \]
Now calculate:
\[ \text{Area of sector} = \left(\frac{4}{9}\right) \times \pi \times 18.49 \]
\[ \text{Area of sector} \approx \left(\frac{4}{9}\right) \times 3.1416 \times 18.49 \]
\[ \text{Area of sector} \approx \left(\frac{4}{9}\right) \times 58.09 \]
\[ \text{Area of sector} \approx 25.827 \text{ cm}^2 \]
Rounded to the nearest tenth:
\[ \text{Area of sector} \approx 25.8 \text{ cm}^2 \]
Therefore, the correct option is:
- ○ 25.8 cm²
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