Final answer:
To find the area of a perfectly circular lake, we use the formula A = πr², where A is the area and r is the radius. By dividing the shoreline length by 2π and converting miles to kilometers, we can calculate the radius in kilometers.
Step-by-step explanation:
To find the area of a perfectly circular lake, we can use the formula for the area of a circle. The formula is A = πr², where A is the area and r is the radius of the circle.
Since we know the shoreline length of Lake Superior, we can use this information to find the radius. The shoreline length is equivalent to the circumference of the circle, which is given by C = 2πr.
Therefore, the radius, r, is equal to the shoreline length divided by 2π. r = 2726 miles / (2π).
To convert miles to kilometers, we can multiply by the conversion factor of 1.609, since 1 mile is equal to 1.609 kilometers.
Once we have the radius in kilometers, we can substitute it into the formula for the area of a circle, A = πr², to find the area of Lake Superior.
Therefore, the area of Lake Superior is approximately A = π(2726 miles / (2π))² km² = 69,144 km².