Question
An earthquake was felt throughout a circular area of 1,808.64 square miles. What was the radius of the circular area?
Question 19 options:
A)
20 miles
B)
576 miles
C)
12 miles
D)
24 miles
Question 19 options:
A)
20 miles
B)
576 miles
C)
12 miles
D)
24 miles
Answers
GPT-4o mini
To find the radius of a circular area given its area, we can use the formula for the area of a circle:
\[
A = \pi r^2
\]
where \( A \) is the area and \( r \) is the radius.
Given the area is 1,808.64 square miles, we can set up the equation:
\[
\pi r^2 = 1808.64
\]
To solve for \( r^2 \), we first divide both sides by \(\pi\):
\[
r^2 = \frac{1808.64}{\pi}
\]
Using \(\pi \approx 3.14\):
\[
r^2 \approx \frac{1808.64}{3.14} \approx 576
\]
Now, we take the square root to find \( r \):
\[
r \approx \sqrt{576} = 24
\]
So, the radius of the circular area is approximately 24 miles.
Thus, the correct answer is:
**D) 24 miles**
\[
A = \pi r^2
\]
where \( A \) is the area and \( r \) is the radius.
Given the area is 1,808.64 square miles, we can set up the equation:
\[
\pi r^2 = 1808.64
\]
To solve for \( r^2 \), we first divide both sides by \(\pi\):
\[
r^2 = \frac{1808.64}{\pi}
\]
Using \(\pi \approx 3.14\):
\[
r^2 \approx \frac{1808.64}{3.14} \approx 576
\]
Now, we take the square root to find \( r \):
\[
r \approx \sqrt{576} = 24
\]
So, the radius of the circular area is approximately 24 miles.
Thus, the correct answer is:
**D) 24 miles**