Final answer:
The area of the largest circular sheep pen that can be built with 100 ft. of fencing, using 3.14 for Pi, is approximately 796.19 square feet.
Step-by-step explanation:
The student has 100 ft. of fencing to use for constructing a circular sheep pen and is asked to find the area of the largest pen they can build using 3.14 for Pi. To start, we know the circumference (C) formula is C = Pi * d, where d is the diameter of the circle. Since the student has 100 ft. of fencing for the circumference, we can set up the equation 100 = 3.14 * d to find the diameter. Solving for d, we get d = 100 / 3.14, which is approximately 31.85 ft.
Once we have the diameter, we can find the radius (r) by dividing the diameter by 2, giving us r = 31.85 / 2, which is approximately 15.92 ft. Then, we can use the area (A) formula for a circle, which is A = Pi * r^2. Plugging in the radius we found into the area formula gives us A = 3.14 * (15.92)^2, which calculates to A = 3.14 * 253.5664, or an area of approximately 796.19 square feet.