Answer:
1. Radius: 30 yards
2. Cost per square yard: $7,065
Step-by-step explanation:
The formula to find the area of quarter circle is:
[tex]A=\frac{\pi r^2}{4}[/tex]
Where "r" is the radius.
Solving for "r":
[tex]r=\sqrt{\frac{4A}{\pi}}[/tex]
1. Find the area of the playground with the formula for calculate the area of a square:
[tex]A=s^2[/tex]
Where "s" is the side lenght.
Since:
[tex]s=109\ yd[/tex]
You get:
[tex]A_1=(109\ yd)^2=11,881\ yd^2[/tex]
All the skating rings are equal.
So, knowing that the area of the remaining field is:
[tex]A_3=9,055\ yd^2[/tex]
The sum of the areas of all the quarter circles is:
[tex]A_4=11,881\ yd^2-9,055\ yd^2=2,826\ yd^2[/tex]
To find the area of each skating ring, divide that result by 4:
[tex]A_4=\frac{2,826\ yd^2}{4}= 706.5\ yd^2[/tex]
Then, the radius is:
[tex]r=\sqrt{\frac{4(706.5\ yd^2)}{3.14}}=30\ yd[/tex]
2. Mulitply the total area of the skating rings by $2.50 in order to find the cost of cementing the skating rings per square yard:
[tex]Cost\ per\ square\ yard=2,826*\$2.50=\$7,065[/tex]
