The area of the sector below is 26.15 m² 9 m Calculate the value of the angle x
Advanced Engineering Mathematics
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ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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![**Question 5:**
The problem states that the area of the sector below is \( 26.15 \, \text{m}^2 \).
A diagram is provided showing a sector of a circle with a radius of 9 meters. The angle of the sector is marked as \( x^\circ \).
- **Task:** Calculate the value of the angle \( x \).
- **Instructions:** Provide your answer to one decimal place.
- **Marks:** [2 marks]
(Level 5)
---
**Question 6:**
The diagram presents an equilateral triangle with each side measuring 9 cm.
Within this triangle, sector \( OAB \) is shaded. \( O \) is the center of a circle, and the sector \( OAB \) is part of this circle with \( OA = 3 \, \text{cm} \). The angle of the sector is marked as \( x^\circ \).
- **Task:** Find the perimeter of the shaded region.
- **Instructions:** Give your answer to one decimal place.
- **Marks:** [3 marks]
(Level 6)
**Note:** Diagrams labelled as "Not drawn accurately" indicate that dimensions and angles may not be to scale in the illustrations provided.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fefb432e6-9285-4a0a-ad1e-00bcc4d31784%2Fa2145e85-2a2b-4cbe-b872-d398fdbead88%2Fmi15ffr_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Question 5:**
The problem states that the area of the sector below is \( 26.15 \, \text{m}^2 \).
A diagram is provided showing a sector of a circle with a radius of 9 meters. The angle of the sector is marked as \( x^\circ \).
- **Task:** Calculate the value of the angle \( x \).
- **Instructions:** Provide your answer to one decimal place.
- **Marks:** [2 marks]
(Level 5)
---
**Question 6:**
The diagram presents an equilateral triangle with each side measuring 9 cm.
Within this triangle, sector \( OAB \) is shaded. \( O \) is the center of a circle, and the sector \( OAB \) is part of this circle with \( OA = 3 \, \text{cm} \). The angle of the sector is marked as \( x^\circ \).
- **Task:** Find the perimeter of the shaded region.
- **Instructions:** Give your answer to one decimal place.
- **Marks:** [3 marks]
(Level 6)
**Note:** Diagrams labelled as "Not drawn accurately" indicate that dimensions and angles may not be to scale in the illustrations provided.
![**Question 4:**
The sector of a circle below has a radius of 5m and the angle at the center is 30°.
(Level 5)
A diagram shows a sector of a circle with a central angle of 30° and a radius of 5 m. The diagram is annotated with "Not drawn accurately."
**Part 4(a):**
Find the area of the sector.
Give your answer to one decimal place.
\[2 \text{ marks}\]
\[ \text{Answer: } \quad \_\_\_\_\_\_\_\_\_\_ \quad \text{cm}^2 \]
**Part 4(b):**
Find the arc length of the sector.
Give your answer to one decimal place.
\[2 \text{ marks}\]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fefb432e6-9285-4a0a-ad1e-00bcc4d31784%2Fa2145e85-2a2b-4cbe-b872-d398fdbead88%2Fskm2mxf_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Question 4:**
The sector of a circle below has a radius of 5m and the angle at the center is 30°.
(Level 5)
A diagram shows a sector of a circle with a central angle of 30° and a radius of 5 m. The diagram is annotated with "Not drawn accurately."
**Part 4(a):**
Find the area of the sector.
Give your answer to one decimal place.
\[2 \text{ marks}\]
\[ \text{Answer: } \quad \_\_\_\_\_\_\_\_\_\_ \quad \text{cm}^2 \]
**Part 4(b):**
Find the arc length of the sector.
Give your answer to one decimal place.
\[2 \text{ marks}\]
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