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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Find the indicated measure. Round to the nearest tenth.
![### Geometry Problem: Finding the Radius of a Circle
**Problem Statement:**
6. The area of a circle is 706.9 square inches. Find the radius.
**Explanation and Solution:**
To find the radius of the circle, we need to use the formula for the area of a circle. The area \( A \) of a circle is given by:
\[ A = \pi r^2 \]
where \( \pi \) (pi) is approximately 3.14159, and \( r \) is the radius of the circle.
Given that the area \( A \) is 706.9 square inches, we can set up the equation:
\[ 706.9 = \pi r^2 \]
To solve for the radius \( r \), follow these steps:
1. **Divide both sides by \( \pi \):**
\[ \frac{706.9}{\pi} = r^2 \]
2. **Calculate \( \frac{706.9}{\pi} \):**
\[ \frac{706.9}{3.14159} \approx 225 \]
3. **Take the square root of both sides:**
\[ r = \sqrt{225} \]
4. **Simplify:**
\[ r = 15 \]
**Answer:**
The radius of the circle is **15 inches**.
Understanding these steps will help you solve similar problems involving the area and radius of circles.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F3fb3a75e-23bc-4bdf-ae48-0fbed2f873b0%2F54985abe-7a8a-4983-8488-dec25920ee09%2Fugy7xt_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Geometry Problem: Finding the Radius of a Circle
**Problem Statement:**
6. The area of a circle is 706.9 square inches. Find the radius.
**Explanation and Solution:**
To find the radius of the circle, we need to use the formula for the area of a circle. The area \( A \) of a circle is given by:
\[ A = \pi r^2 \]
where \( \pi \) (pi) is approximately 3.14159, and \( r \) is the radius of the circle.
Given that the area \( A \) is 706.9 square inches, we can set up the equation:
\[ 706.9 = \pi r^2 \]
To solve for the radius \( r \), follow these steps:
1. **Divide both sides by \( \pi \):**
\[ \frac{706.9}{\pi} = r^2 \]
2. **Calculate \( \frac{706.9}{\pi} \):**
\[ \frac{706.9}{3.14159} \approx 225 \]
3. **Take the square root of both sides:**
\[ r = \sqrt{225} \]
4. **Simplify:**
\[ r = 15 \]
**Answer:**
The radius of the circle is **15 inches**.
Understanding these steps will help you solve similar problems involving the area and radius of circles.
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