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
Related questions
Question
Find the area for circles
![**Problem 6: Understanding Circle Measurements**
Given the following diagram:
[Insert Image of Circle Here]
In the diagram, we have a circle with a radius clearly marked as 15.6 cm. The radius is the distance from the center of the circle to any point on its perimeter.
**Key Information:**
- **Radius (r):** 15.6 cm
**Explanation of Diagrams:**
The diagram consists of a simple circle with a line segment originating from the center and reaching out to the edge of the circle. This line segment represents the radius of the circle, which is labeled as "15.6 cm."
**Mathematical Context:**
1. **Circumference of the Circle (C):**
To find the circumference, we use the formula:
\[
C = 2\pi r
\]
Plugging in the value of the radius:
\[
C = 2\pi(15.6 \text{ cm}) \approx 98.0 \text{ cm}
\]
2. **Area of the Circle (A):**
To find the area, we use the formula:
\[
A = \pi r^2
\]
Plugging in the value of the radius:
\[
A = \pi (15.6 \text{ cm})^2 \approx 764.5 \text{ cm}^2
\]
Understanding these basic properties of circles is essential in geometry and is applicable in various real-life scenarios, such as designing wheels, clocks, and any other round shapes.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F467ecbdb-fd5b-4b4c-ab67-30d508e676d8%2F109c3897-f549-4c2e-b797-d72e22157df6%2Ffjlbo88_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Problem 6: Understanding Circle Measurements**
Given the following diagram:
[Insert Image of Circle Here]
In the diagram, we have a circle with a radius clearly marked as 15.6 cm. The radius is the distance from the center of the circle to any point on its perimeter.
**Key Information:**
- **Radius (r):** 15.6 cm
**Explanation of Diagrams:**
The diagram consists of a simple circle with a line segment originating from the center and reaching out to the edge of the circle. This line segment represents the radius of the circle, which is labeled as "15.6 cm."
**Mathematical Context:**
1. **Circumference of the Circle (C):**
To find the circumference, we use the formula:
\[
C = 2\pi r
\]
Plugging in the value of the radius:
\[
C = 2\pi(15.6 \text{ cm}) \approx 98.0 \text{ cm}
\]
2. **Area of the Circle (A):**
To find the area, we use the formula:
\[
A = \pi r^2
\]
Plugging in the value of the radius:
\[
A = \pi (15.6 \text{ cm})^2 \approx 764.5 \text{ cm}^2
\]
Understanding these basic properties of circles is essential in geometry and is applicable in various real-life scenarios, such as designing wheels, clocks, and any other round shapes.
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