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.
