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 in terms of pi and answer both questions separately they're two parts in one question.
![### Finding the Area of a Circle
To calculate the area of a circle, use the following formula:
\[ \text{Area} = \pi r^2 \]
Where:
- \( \pi \) is a constant (approximately 3.14159)
- \( r \) is the radius of the circle
### Example Problems
#### Problem 9:
A circle with a diameter labeled as **1.7 feet**.
**Solution:**
1. First, find the radius. The radius \( r \) is half of the diameter.
\[ r = \frac{1.7 \text{ ft}}{2} = 0.85 \text{ ft} \]
2. Then use the formula to find the area.
\[ \text{Area} = \pi (0.85 \text{ ft})^2 \]
\[ \text{Area} = \pi (0.7225) \text{ ft}^2 \]
\[ \text{Area} \approx 2.27 \pi \text{ ft}^2 \]
#### Problem 10:
A circle with a diameter labeled as \( \frac{2}{3} \) inches.
**Solution:**
1. First, find the radius. The radius \( r \) is half of the diameter.
\[ r = \frac{\frac{2}{3} \text{ in}}{2} = \frac{1}{3} \text{ in} \]
2. Then use the formula to find the area.
\[ \text{Area} = \pi \left( \frac{1}{3} \text{ in} \right)^2 \]
\[ \text{Area} = \pi \left( \frac{1}{9} \right) \text{ in}^2 \]
\[ \text{Area} = \frac{\pi}{9} \text{ in}^2 \]
### Diagrams Explanation
**Diagram 9:**
- A circle with a diameter measuring 1.7 feet is shown. This requires computing the radius as half of the diameter to then find the area using the area formula.
**Diagram 10:**
- A circle with a diameter measuring \( \frac{2}{3} \) inches is displayed. Similarly, the radius is determined by halving the diameter](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F9359044e-f021-4fc6-a0ad-5a2dc758cf44%2F175a15b0-594b-4fa1-b1cb-3926d860eb3b%2Fiq8ktep_processed.png&w=3840&q=75)
Transcribed Image Text:### Finding the Area of a Circle
To calculate the area of a circle, use the following formula:
\[ \text{Area} = \pi r^2 \]
Where:
- \( \pi \) is a constant (approximately 3.14159)
- \( r \) is the radius of the circle
### Example Problems
#### Problem 9:
A circle with a diameter labeled as **1.7 feet**.
**Solution:**
1. First, find the radius. The radius \( r \) is half of the diameter.
\[ r = \frac{1.7 \text{ ft}}{2} = 0.85 \text{ ft} \]
2. Then use the formula to find the area.
\[ \text{Area} = \pi (0.85 \text{ ft})^2 \]
\[ \text{Area} = \pi (0.7225) \text{ ft}^2 \]
\[ \text{Area} \approx 2.27 \pi \text{ ft}^2 \]
#### Problem 10:
A circle with a diameter labeled as \( \frac{2}{3} \) inches.
**Solution:**
1. First, find the radius. The radius \( r \) is half of the diameter.
\[ r = \frac{\frac{2}{3} \text{ in}}{2} = \frac{1}{3} \text{ in} \]
2. Then use the formula to find the area.
\[ \text{Area} = \pi \left( \frac{1}{3} \text{ in} \right)^2 \]
\[ \text{Area} = \pi \left( \frac{1}{9} \right) \text{ in}^2 \]
\[ \text{Area} = \frac{\pi}{9} \text{ in}^2 \]
### Diagrams Explanation
**Diagram 9:**
- A circle with a diameter measuring 1.7 feet is shown. This requires computing the radius as half of the diameter to then find the area using the area formula.
**Diagram 10:**
- A circle with a diameter measuring \( \frac{2}{3} \) inches is displayed. Similarly, the radius is determined by halving the diameter
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