Question

Question 7.A groundskeeper needs grass seed to cover a circular field, 290 feet in diameter. A store sells 50-pound bags of grass seed. One pound of grass seed covers about 400 square feet of field. What is the smallest number of bags the groundskeeper must buy to cover the circular field? Explain or show your reasoning

Answer 1

Hello there. To solve this question, we'll need to remember how to find the area of a circular region and calculate how many grass seed bags we'll need to cover this region.

First, given the diameter D of a circular region, its area can be calculated by the formula: A = pi * D²/4

Such that, knowing that D = 290 feet, we'll get:

A = pi * 290²/4 = 21025pi

Using pi approx. 3.14159, we'll have:

A approx. 66052 feet²

Now, we know that a one pound of grass seedcovers about 400 square feet of the field.

Dividing the area by 400, we'll get the amount of pounds needed to cover this field:

66052/400 approx. 165

Finally, dividing it by 50, we'll get the amount of 50-pound bags of grass seed we'll need:

165/50 approx 3.3

Since we can't buy another type of bag, the smallest number of bags the groundskeeper must buy to cover this circular field is 4.