Question

You have 100 ft. of fencing to build a circular sheep pen. What is the area of the largest pen you can build? (use 3.14 for Pi)

A) 785 sq. ft.
B) 795 sq. ft.
C) 805 sq. ft.
D) 815 sq. ft.

Answer 1

To find the area of the largest circular pen, calculate the radius using the formula for the circumference of a circle and substitute it into the area formula. The result is approximately 795 sq. ft.

Step-by-step explanation:

To find the area of the largest circular pen using 100 ft of fencing, we need to maximize the area of the circle. The formula for the area of a circle is A = πr², where π is approximately 3.14 and r is the radius. Since the perimeter (length around) of the circle is equal to the length of the fencing, we can calculate the radius using the formula for the circumference of a circle, C = 2πr. In this case, C = 100 ft, so 100 = 2πr. Solving for r gives us r = 100 / (2π) = 50 / π. Substituting this value into the area formula, we get A = π(50 / π)² = (50² / π) ft². Evaluating this expression gives us approximately 795 sq. ft., so the answer is B) 795 sq. ft.