### Find the Area of the Shaded SectorThis problem involves calculating the area of a shaded sector within a circle.#### Diagram Explanation:- The diagram is of a circle centered at point O.- The radius of the circle is labeled as 10 units.- An angle of 18 degrees is formed at the center, corresponding to the shaded sector.#### Steps to Calculate the Area of the Shaded Sector:1. **Understand the formula**: The area $ A $ of a sector of a circle can be determined using the following formula: \[ A = \frac{\theta}{360} \times \pi r^2 \] where: - $\theta$ is the central angle in degrees. - $r$ is the radius of the circle.2. **Substitute the values**: Here, $\theta = 18^\circ$ and $r = 10$. So, we substitute these values into the formula: \[ A = \frac{18}{360} \times \pi \times 10^2 \]3. **Simplify the fractions**: \[ A = \frac{1}{20} \times \pi \times 100 \]4. **Calculate the area**: \[ A = 5\pi \]Hence, the area of the shaded sector is $ 5\pi $ square units.#### Final AnswerThe area of the shaded sector is $ 5\pi $ square units.

Our Aim is to find the Area of the shaded sector.

Answered: Find the area of the shaded sector.

Math

Geometry

Find the area of the shaded sector.

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 the Shaded Sector

This problem involves calculating the area of a shaded sector within a circle.

#### Diagram Explanation:
- The diagram is of a circle centered at point O.
- The radius of the circle is labeled as 10 units.
- An angle of 18 degrees is formed at the center, corresponding to the shaded sector.

#### Steps to Calculate the Area of the Shaded Sector:

1. **Understand the formula**:
The area $ A $ of a sector of a circle can be determined using the following formula:
\[
A = \frac{\theta}{360} \times \pi r^2
\]
where:
- $\theta$ is the central angle in degrees.
- $r$ is the radius of the circle.

2. **Substitute the values**:
Here, $\theta = 18^\circ$ and $r = 10$.

So, we substitute these values into the formula:
\[
A = \frac{18}{360} \times \pi \times 10^2
\]

3. **Simplify the fractions**:
\[
A = \frac{1}{20} \times \pi \times 100
\]

4. **Calculate the area**:
\[
A = 5\pi
\]

Hence, the area of the shaded sector is $ 5\pi $ square units.

#### Final Answer
The area of the shaded sector is $ 5\pi $ square units.

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