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 = 3.14.

Answer 1

Part 1)
`r=30\ yd`

Part 2)
`\$7.065`

Explanation:

Part 1)

Find the radius of each skating rink

we know that

The area of the playground (complete square) minus the area of four quarter of circle (one complete circle) must be equal to 9,055 square yards

so

`9,055=(109^2)-\pi r^(2)`

Solve for r

`9,055=11,881-\pi r^(2)`

`\pi r^(2)=11,881-9,055`

`\pi r^(2)=2,826`

substitute the value of pi

`(3.14)r^(2)=2,826`

`r^(2)=2,826/3.14`

`r^(2)=900`

`r=30\ yd`

Part 2) Find the cost of cementing the skating rinks

Multiply the area of one circle (four quarters) by $2.50 per square yards

`(3.14)(30^2)(2.50)=\$7.065`