Elementary Algebra
17th Edition
ISBN:9780998625713
Author:Lynn Marecek, MaryAnne Anthony-Smith
Publisher:Lynn Marecek, MaryAnne Anthony-Smith
Chapter9: Roots And Radicals
Section9.4: Multiply Square Roots
Problem 313E: A garden will be made so as to contain two square sections, one section with side length 5+6 yards...
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![**Problem:**
The circumference of a circle is \(7\pi\) ft. What is the area, in square feet? Express your answer in terms of \(\pi\).
**Solution:**
To solve for the area of the circle, we start by using the given circumference formula:
\[ C = 2\pi r \]
Given \( C = 7\pi \) ft:
\[ 2\pi r = 7\pi \]
Divide both sides by \(2\pi\):
\[ r = \frac{7\pi}{2\pi} = \frac{7}{2} \]
Therefore, the radius \( r \) is \( \frac{7}{2} \) ft.
Now, use the formula for the area \( A \) of a circle:
\[ A = \pi r^2 \]
Substitute \( r = \frac{7}{2} \):
\[ A = \pi \left(\frac{7}{2}\right)^2 = \pi \left(\frac{49}{4}\right) = \frac{49\pi}{4} \]
Thus, the area of the circle is:
\[ \boxed{\frac{49\pi}{4}} \] square feet.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F16ab444c-cc67-4b2e-a5c5-3a02b2df29f8%2F275dcb84-71dc-4baa-b604-319189ac8f6c%2Fdqe6tdp_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Problem:**
The circumference of a circle is \(7\pi\) ft. What is the area, in square feet? Express your answer in terms of \(\pi\).
**Solution:**
To solve for the area of the circle, we start by using the given circumference formula:
\[ C = 2\pi r \]
Given \( C = 7\pi \) ft:
\[ 2\pi r = 7\pi \]
Divide both sides by \(2\pi\):
\[ r = \frac{7\pi}{2\pi} = \frac{7}{2} \]
Therefore, the radius \( r \) is \( \frac{7}{2} \) ft.
Now, use the formula for the area \( A \) of a circle:
\[ A = \pi r^2 \]
Substitute \( r = \frac{7}{2} \):
\[ A = \pi \left(\frac{7}{2}\right)^2 = \pi \left(\frac{49}{4}\right) = \frac{49\pi}{4} \]
Thus, the area of the circle is:
\[ \boxed{\frac{49\pi}{4}} \] square feet.
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