The cheerleaders designed a banner for the homecoming game. It has 3 congruent circles glued on a rectangular length of poster board. The circles touch the edges of the paper and do not overlap.
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If the poster is 36 inches long, what is the area of one circle?
a
37.68 in2
b
113.04in2
c
452.16 in2
d
18.84 in2
To find the area of one circle, we need to know the radius of the circle.
Given that the circles touch the edges of the paper and do not overlap, we can deduce that the width of the rectangular paper is twice the diameter of the circle.
Since the length of the rectangular paper is 36 inches, we can divide it by 2 to find the diameter of one circle.
36 inches ÷ 2 = 18 inches
The radius of the circle is half the diameter, so the radius of one circle is 18 inches ÷ 2 = 9 inches.
Now that we have the radius, we can find the area of the circle using the formula:
Area = π * radius^2
Plugging in the value of the radius:
Area = π * 9^2
= π * 81
Since we are not given the exact value of π, we can use an approximation of π as 3.14.
Area ≈ 3.14 * 81
≈ 254.34 in^2
So, the area of one circle is approximately 254.34 in^2.
Therefore, none of the given options (a, b, c, d) matches the correct answer.