Final answer:
The groundskeeper can enclose an area of approximately 4984.52 square feet with 250 feet of fencing.
Step-by-step explanation:
To find the area that the groundskeeper can enclose with 250 feet of fencing, we need to determine the circumference of the circular flower bed.
The formula to find the circumference of a circle is C = 2πr, where C is the circumference and r is the radius.
In this case, the circumference is equal to the amount of fencing the groundskeeper has, which is 250 feet. So we can set up the equation as follows:
250 = 2πr
To solve for the radius, we divide both sides of the equation by 2π:
r = 250 / (2π)
Using the value of π as approximately 3.14, we can calculate the radius:
r ≈ 250 / (2 x 3.14) ≈ 250 / 6.28 ≈ 39.81 feet
Finally, to find the area of the circular flower bed, we use the formula A = πr^2, where A is the area and r is the radius:
A ≈ 3.14 x 39.81^2 ≈ 3.14 x 1585.56 ≈ 4984.52 square feet