Answer:
radius = 30 yd
, cost of cement = $7065
Step-by-step explanation:
First we will 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
The four quarter-circle skating rinks add to a total area of a full circle. That area is given by ...
A = πr^2
Put the values in the formula:
2826 = 3.14r^2
Divide both sides by 3.14
900 = r^2
By taking square root at both sides we get,
30 = r
The radius of each quadrant is 30 yards....
