Answer:
67 bags of sand
Explanation:
First, we need to calculate the area of the path. So, this area can be calculated as the difference between the area of the circle with a diameter of 36 yd and the area of the circle with 28 yd.
The area of a circle can be calculated as:
[tex]A=\pi\cdot r^2[/tex]Where π is 3.14 and r is the radius of the circle.
The radius of a circle is half the diameter. So, the radius of the circle with a diameter of 36 yd is 18 yd and its area is:
[tex]\begin{gathered} A_1=3.14\times(18)^2 \\ A_1=1017.36yd^2 \end{gathered}[/tex]In the same way, the radius of the circle with a diameter of 28 yd is 14 yd and its area is equal to:
[tex]\begin{gathered} A_2=3.14\times(14)^2 \\ A_2=615.44yd^2 \end{gathered}[/tex]Then, the area of the path is equal to:
[tex]\begin{gathered} A_1-A_2=1017.36-615.44 \\ A_1-A_2=401.92yd^2 \end{gathered}[/tex]Now, the number of bags of sand can be calculated as:
[tex]\text{Bags = }\frac{401.82yd^2}{6yd^2}=66.98\approx67\text{ bags of sand}[/tex]Because each bag of sand covers 6 yd².
Therefore, the gardener needs 67 bags of sand
