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 (pie=3.14).

Answer 1

Answer:

• radius = 30 yd
• cost of cement = $7065

Step-by-step explanation:

First we find the area of the circular sectors. From that we can find the cost of cement and their radius.

The area of the playground is ...

  playground area = (109 yd)^2 = 11,881 yd^2

Then the area of the skating rinks is ...

  rink area = playground area - remaining field

  rink area = 11,881 yd^2 - 9,055 yd^2 = 2,826 yd^2

Then the cost of cement for the rink area is ...

  (2826 yd^2)($2.50/yd^2) = $7065

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The four quarter-circle skating rinks add to a total area of a full circle. That area is given by ...

  A = πr^2

Substituting what we know, we have ...

  2826 = 3.14r^2

  900 = r^2 . . . . . . . . divide by 3.14

  30 = r . . . . . . . . . . . take the square root

The radius of each quadrant is 30 yards.