The area of the sector below is 26.15 m² 9 m Calculate the value of the angle x

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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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.
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.

\[2 \text{ marks}\]
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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