A circular lake has a circumference of 24 miles. To the nearest square mile, what is the area of the lake?
A.
15 square miles
B.
46 square miles
C.
183 square miles
D.
452 square miles
A. 15 square miles
To find the area of the lake, we first need to find the radius. Since \(C = 2 \times \pi \times r\), we have:
\(24 = 2 \times \pi \times r\)
\(r = \frac{24}{2\pi} \approx 3.82\)
Now we can find the area of the lake using the formula \(A = \pi \times r^2\):
\(A = \pi \times (3.82)^2 \approx 45.8\) square miles
Rounding to the nearest square mile, the area of the lake is 46 square miles, which corresponds to answer choice B.