Final answer:
The maximum area enclosed by a 250 ft fence in a circular shape is 15625 / π ft², calculated by relating the circumference with the radius and then using the formula for the area of a circle.
Step-by-step explanation:
The question is about calculating the area that can be enclosed by a circular fence with a circumference of 250 ft. To determine this area, we need to relate the fence length, which is the circumference of the circle (C), to the radius (r), and then use the area formula for a circle A = πr2.
The formula for the circumference of a circle is C = 2πr. Given that C = 250 ft, we can solve for the radius:
- C = 2πr
- 250 ft = 2πr
- r = 250 ft / (2π)
Now, using the formula for area, A = πr2, and substituting the value of r we found:
- A = π(250 / (2π))2
- A = (2502) / (4π) ft2
- A = 62500 / (4π) ft2
- A = 15625 / π ft2
The maximum area that can be enclosed is 15625 / π ft2.
Remember that when dealing with significant figures in calculations, the final result should only be as precise as the least precise measurement in the data provided.