Question

A playground is in the shape of a square with each side equal to 109 yards. It has skating rinks in the shape of the quadrants of a circle at each corner. If the area of the remaining field is 9055, find the radius of each skating rink. Also, find the cost of cementing the skating rinks at $2.50 per square yards. Use π = 3.14

Answer 1

1. Radius: 30 yards

2. Cost per square yard: $7,065

Explanation:

The formula to find the area of quarter circle is:

`A=(\pi r^2)/(4)`

Where "r" is the radius.

Solving for "r":

`r=\sqrt{(4A)/(\pi)}`

1. Find the area of the playground with the formula for calculate the area of a square:

`A=s^2`

Where "s" is the side lenght.

Since:

`s=109\ yd`

You get:

`A_1=(109\ yd)^2=11,881\ yd^2`

All the skating rings are equal.

So, knowing that the area of the remaining field is:

`A_3=9,055\ yd^2`

The sum of the areas of all the quarter circles is:

`A_4=11,881\ yd^2-9,055\ yd^2=2,826\ yd^2`

To find the area of each skating ring, divide that result by 4:

`A_4=(2,826\ yd^2)/(4)= 706.5\ yd^2`

Then, the radius is:

`r=\sqrt{(4(706.5\ yd^2))/(3.14)}=30\ yd`

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:

`Cost\ per\ square\ yard=2,826*\$2.50=\$7,065`