I need to find the are of the sector if the radius is 8cm **Finding the Area of a Sector****Problem Statement:**Find the area of the sector if the radius is 8 cm.**Diagram Explanation:**The provided diagram depicts a circle with center B. The circle contains a sector ∠ABC, where the angle at the center, AB, is marked as 51°. The radius of the circle, which is the distance from B to any point on the circle (such as A or C), is given as 8 cm.**Step-by-Step Solution:**1. **Identify Given Data:** - Radius (r): 8 cm - Central Angle (θ): 51°2. **Formula for the Area of a Sector:** The area of a sector is given by the formula: \[ \text{Area} = \frac{\theta}{360} \times \pi r^2 \] where: - $ \theta $ is the central angle in degrees. - $ r $ is the radius. - $ \pi $ (pi) is a constant approximately equal to 3.14159.3. **Substitute Values:** Inserting the given values into the formula: \[ \text{Area} = \frac{51}{360} \times \pi \times (8)^2 \]4. **Calculate the Area:** - Calculate $8^2$: \[ 8^2 = 64 \] - Multiply by $ \pi $: \[ 64\pi \] - Fraction of the circle ( $\frac{51}{360}$ ): \[ \frac{51}{360} \approx 0.1417 \] - Finally, multiply all parts together: \[ \text{Area} \approx 0.1417 \times 64\pi \] - Calculating it to two decimal places: \[ \text{Area} \approx 0.1417 \times 201.062 \] \[ \text{Area} \approx 28.5 \text{ cm}^2 \]**Final Answer:**The area of the sector is approximately 28.5 cm².

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Math

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Find the area of the sector if the radius is 8cm B 51

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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I need to find the are of the sector if the radius is 8cm

**Finding the Area of a Sector**

**Problem Statement:**
Find the area of the sector if the radius is 8 cm.

**Diagram Explanation:**
The provided diagram depicts a circle with center B. The circle contains a sector ∠ABC, where the angle at the center, AB, is marked as 51°. The radius of the circle, which is the distance from B to any point on the circle (such as A or C), is given as 8 cm.

**Step-by-Step Solution:**

1. **Identify Given Data:**
- Radius (r): 8 cm
- Central Angle (θ): 51°

2. **Formula for the Area of a Sector:**
The area of a sector is given by the formula:
\[
\text{Area} = \frac{\theta}{360} \times \pi r^2
\]
where:
- $ \theta $ is the central angle in degrees.
- $ r $ is the radius.
- $ \pi $ (pi) is a constant approximately equal to 3.14159.

3. **Substitute Values:**
Inserting the given values into the formula:
\[
\text{Area} = \frac{51}{360} \times \pi \times (8)^2
\]

4. **Calculate the Area:**
- Calculate $8^2$:
\[
8^2 = 64
\]
- Multiply by $ \pi $:
\[
64\pi
\]
- Fraction of the circle ( $\frac{51}{360}$ ):
\[
\frac{51}{360} \approx 0.1417
\]
- Finally, multiply all parts together:
\[
\text{Area} \approx 0.1417 \times 64\pi
\]
- Calculating it to two decimal places:
\[
\text{Area} \approx 0.1417 \times 201.062
\]
\[
\text{Area} \approx 28.5 \text{ cm}^2
\]

**Final Answer:**
The area of the sector is approximately 28.5 cm².

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