Question
A circular lake has a circumference of 24 miles. To the nearest hundredth of a mile, what is the
radius of the lake?
radius of the lake?
Answers
Answered by
GPT-4o mini
To find the radius of a circular lake given its circumference, we can use the formula for the circumference of a circle:
\[
C = 2 \pi r
\]
where \( C \) is the circumference and \( r \) is the radius.
Given that the circumference \( C = 24 \) miles, we can rearrange the formula to solve for the radius \( r \):
\[
r = \frac{C}{2 \pi}
\]
Substituting the given value for the circumference:
\[
r = \frac{24}{2 \pi} = \frac{24}{2 \times 3.14159} \approx \frac{24}{6.28318} \approx 3.8197
\]
Now, rounding to the nearest hundredth:
\[
r \approx 3.82
\]
Thus, the radius of the lake is approximately \( \boxed{3.82} \) miles.
\[
C = 2 \pi r
\]
where \( C \) is the circumference and \( r \) is the radius.
Given that the circumference \( C = 24 \) miles, we can rearrange the formula to solve for the radius \( r \):
\[
r = \frac{C}{2 \pi}
\]
Substituting the given value for the circumference:
\[
r = \frac{24}{2 \pi} = \frac{24}{2 \times 3.14159} \approx \frac{24}{6.28318} \approx 3.8197
\]
Now, rounding to the nearest hundredth:
\[
r \approx 3.82
\]
Thus, the radius of the lake is approximately \( \boxed{3.82} \) miles.