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
![### Circle Measurement Problem
#### Task:
Determine:
- (a) the area of the circle
- (b) the circumference of the circle.
#### Diagram Details:
The diagram shows a circle with a horizontal diameter. The diameter of the circle is labeled as 21 feet.
#### Solution:
To find the area and circumference of the circle, use the following formulas:
1. **Area of the Circle (A)**:
\[
A = \pi \times r^2
\]
Where \( r \) is the radius of the circle. Since the diameter is 21 feet, the radius \( r \) is half of the diameter:
\[
r = \frac{21}{2} = 10.5 \text{ feet}
\]
2. **Circumference of the Circle (C)**:
\[
C = 2 \times \pi \times r
\]
#### Calculations:
- **Area**:
\[
A = \pi \times (10.5)^2 \approx 346.36 \text{ square feet}
\]
- **Circumference**:
\[
C = 2 \times \pi \times 10.5 \approx 65.97 \text{ feet}
\]
These calculations provide the area and circumference of the circle based on the given diameter.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F1658d937-8052-45d3-ba3f-7a589de5c533%2F098be3d0-c7f0-436c-a570-6f28c0e1bfa1%2Fi10d2nc_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Circle Measurement Problem
#### Task:
Determine:
- (a) the area of the circle
- (b) the circumference of the circle.
#### Diagram Details:
The diagram shows a circle with a horizontal diameter. The diameter of the circle is labeled as 21 feet.
#### Solution:
To find the area and circumference of the circle, use the following formulas:
1. **Area of the Circle (A)**:
\[
A = \pi \times r^2
\]
Where \( r \) is the radius of the circle. Since the diameter is 21 feet, the radius \( r \) is half of the diameter:
\[
r = \frac{21}{2} = 10.5 \text{ feet}
\]
2. **Circumference of the Circle (C)**:
\[
C = 2 \times \pi \times r
\]
#### Calculations:
- **Area**:
\[
A = \pi \times (10.5)^2 \approx 346.36 \text{ square feet}
\]
- **Circumference**:
\[
C = 2 \times \pi \times 10.5 \approx 65.97 \text{ feet}
\]
These calculations provide the area and circumference of the circle based on the given diameter.
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