Question

a flower garden is shaped like a circle. its radius is 18 yd. a ring - shaped path goes around the garden. its outer edge is a circle with radius 22 yd. the gardener is going to cover the path with sand. if one bag of sand can cover 7 yd², how many bags of sand does the gardener need? note that sand comes only by the bag, so the number of bags must be a whole number. (use the value 3.14 for π.)

Explanation:

Step1: Calculate the area of the outer circle

The formula for the area of a circle is \(A = \pi r^{2}\). For the outer circle with radius \(r_{1}=22\) yd, \(A_{1}=\pi\times(22)^{2}=3.14\times484 = 1519.76\) \(yd^{2}\)

Step2: Calculate the area of the inner circle

For the inner circle with radius \(r_{2} = 18\) yd, \(A_{2}=\pi\times(18)^{2}=3.14\times324=1017.36\) \(yd^{2}\)

Step3: Calculate the area of the ring - shaped path

The area of the ring (path) \(A=A_{1}-A_{2}\). So \(A = 1519.76- 1017.36=502.4\) \(yd^{2}\)

Step4: Calculate the number of sand bags

If one bag covers \(7\) \(yd^{2}\), then the number of bags \(n=\frac{A}{7}=\frac{502.4}{7}\approx71.77\)

Since the number of bags must be a whole number, we need to round up.

Answer:

\(72\)