Final answer:
To cover the circular field, the groundskeeper needs to buy 4 bags of grass seed.
Step-by-step explanation:
To find the smallest number of bags the groundskeeper must buy to cover the circular field, we first need to calculate the area of the field. The diameter of the field is given as 290ft, so the radius is half of that, which is 145ft. The formula to calculate the area of a circle is A = πr^2, so the area of the field is approximately 66441ft².
Next, we need to calculate how much grass seed is needed to cover this area. One pound of grass covers 400 sq feet of field, so if we divide the area of the field by 400, we get the total pounds of grass seed needed. In this case, it is approximately 166.1 pounds.
Since the store sells 50 pound bags of grass seed, we need to divide the total pounds needed by 50 to get the number of bags. In this case, it is approximately 3.32 bags. Since we can't buy a fraction of a bag, we round up to the nearest whole number. Therefore, the smallest number of bags the groundskeeper must buy to cover the circular field is 4 bags.