Asked by desitne 2.0
A circular lake has a circumference of 24 miles. To the nearest hundredth of a mile, what is the radius of the lake?
Type your response in the box below.
miles
Type your response in the box below.
miles
Answers
Answered by
GPT-4o mini
To find the radius of the lake, we can use the formula for the circumference of a circle, which is given by:
\[
C = 2\pi r
\]
where \(C\) is the circumference and \(r\) is the radius. Given that the circumference \(C\) is 24 miles, we can solve for the radius \(r\):
\[
24 = 2\pi r
\]
To isolate \(r\), we can divide both sides of the equation by \(2\pi\):
\[
r = \frac{24}{2\pi} = \frac{12}{\pi}
\]
Now, we will calculate the value of \(r\) using the value of \(\pi \approx 3.14159\):
\[
r \approx \frac{12}{3.14159} \approx 3.8197
\]
Rounding this value to the nearest hundredth:
\[
r \approx 3.82
\]
Thus, the radius of the lake is approximately:
\[
\boxed{3.82} \text{ miles}
\]
\[
C = 2\pi r
\]
where \(C\) is the circumference and \(r\) is the radius. Given that the circumference \(C\) is 24 miles, we can solve for the radius \(r\):
\[
24 = 2\pi r
\]
To isolate \(r\), we can divide both sides of the equation by \(2\pi\):
\[
r = \frac{24}{2\pi} = \frac{12}{\pi}
\]
Now, we will calculate the value of \(r\) using the value of \(\pi \approx 3.14159\):
\[
r \approx \frac{12}{3.14159} \approx 3.8197
\]
Rounding this value to the nearest hundredth:
\[
r \approx 3.82
\]
Thus, the radius of the lake is approximately:
\[
\boxed{3.82} \text{ miles}
\]