Final answer:
The correct amount of soil needed would be approximately 31 bags, given that 1 pound of soil covers 10 square feet and each bag weighs 40 pounds. The area of the circular field which is 125 feet in diameter is approximately 12,271.85 square feet. The provided options did not include the correct number of bags required.
Step-by-step explanation:
To find out how many bags of soil the farmer must buy, we first need to calculate the area of the circular field and then determine the total weight of soil needed. The diameter of the field is 125 feet. The formula for the area of a circle is πr², where r is the radius (½ the diameter).
First, calculate the radius: radius = diameter / 2 = 125ft / 2 = 62.5ft
Next, calculate the area of the field: Area = π * (62.5ft)² ≈ 3.14159 * (3906.25ft²) ≈ 12271.85 ft² (approximately).
Now, one pound of soil covers 10 square feet, so the total weight of soil needed is: Total weight = Area / 10 = 12271.85ft² / 10 ≈ 1227.185 pounds.
Finally, since each bag contains 40 pounds of soil, we calculate the number of bags required: Number of bags = Total weight / 40 pounds/bag = 1227.185 pounds / 40 pounds/bag ≈ 30.68 bags.
Since the farmer can only buy whole bags, we round up to the nearest whole number, which means the farmer must buy 31 bags of soil. However, none of the options given (a) 50 bags, (b) 125 bags, (c) 400 bags, and (d) 500 bags) match the correct answer. It's possible there may be an error in the options provided.