Final answer:
To cover a circular field 290 feet in diameter with grass seed, the groundskeeper must calculate the area, determine the total pounds of seed needed, and then divide by the bag size. After these calculations, the groundkeeper needs to buy a minimum of 4 bags of grass seed.
Step-by-step explanation:
To determine the smallest number of bags of grass seed the groundskeeper needs to buy, we first calculate the area of the circular field. The diameter is given as 290 feet, so the radius (r) is half of that, which is 145 feet.
The area (A) of a circle is given by the formula A = πr², where π (pi) is approximately 3.14159. So the area the groundskeeper needs to cover is:
A = π(145 feet)² ≈ 3.14159 × (145²) ≈ 3.14159 × 21025 ≈ 66,069 square feet.
Since 1 pound of grass seed covers about 400 square feet, the total pounds needed to cover the field is:
Total pounds = 66,069 ft² ÷ 400 ft²/pound ≈ 165.17 pounds.
Grass seed is sold in 50-pound bags, so the number of bags needed is:
Number of bags = Total pounds ÷ 50 pounds/bag ≈ 165.17 ÷ 50 ≈ 3.3 bags.
Since we can't purchase a fraction of a bag, the groundskeeper must buy 4 bags to ensure the entire field is covered.