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
![**Question:** The circumference of a circle is \(11\pi\) ft. What is the area, in square feet? Express your answer in terms of \(\pi\).
**Solution:**
Given the circumference of the circle, \(C = 11\pi\) ft.
We know the formula for the circumference of a circle is:
\[ C = 2\pi r \]
From this, we can solve for the radius \(r\):
\[ 11\pi = 2\pi r \]
\[ r = \frac{11\pi}{2\pi} \]
\[ r = \frac{11}{2} \]
\[ r = 5.5 \text{ ft} \]
Next, we use the radius to find the area of the circle. The formula for the area of a circle is:
\[ A = \pi r^2 \]
Substituting the radius into this formula:
\[ A = \pi (5.5)^2 \]
\[ A = \pi (30.25) \]
\[ A = 30.25\pi \text{ square feet} \]
Therefore, the area of the circle is:
\[ \boxed{30.25\pi \text{ square feet}} \]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F16ab444c-cc67-4b2e-a5c5-3a02b2df29f8%2F439dc4b3-3c8d-454b-b318-cab0becc14dc%2F1z3ayh7_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Question:** The circumference of a circle is \(11\pi\) ft. What is the area, in square feet? Express your answer in terms of \(\pi\).
**Solution:**
Given the circumference of the circle, \(C = 11\pi\) ft.
We know the formula for the circumference of a circle is:
\[ C = 2\pi r \]
From this, we can solve for the radius \(r\):
\[ 11\pi = 2\pi r \]
\[ r = \frac{11\pi}{2\pi} \]
\[ r = \frac{11}{2} \]
\[ r = 5.5 \text{ ft} \]
Next, we use the radius to find the area of the circle. The formula for the area of a circle is:
\[ A = \pi r^2 \]
Substituting the radius into this formula:
\[ A = \pi (5.5)^2 \]
\[ A = \pi (30.25) \]
\[ A = 30.25\pi \text{ square feet} \]
Therefore, the area of the circle is:
\[ \boxed{30.25\pi \text{ square feet}} \]
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