A bicycle tire decoration covers 1/9 of the circle formed by the tire. If the tire has a diameter of 26 inches, what is the area of the decoration?
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To find the area of the decoration, we first need to find the area of the entire circle.
The formula to find the area of a circle is A = πr^2, where A represents the area, and r represents the radius of the circle.
Given that the tire has a diameter of 26 inches, we can find the radius by dividing the diameter by 2.
Radius (r) = Diameter / 2 = 26 inches / 2 = 13 inches
Now, we can find the area of the entire circle by plugging the value of the radius into the formula:
A = πr^2 = π(13 inches)^2
≈ 3.14159 * (13 inches)^2
≈ 3.14159 * 169 inches^2
≈ 530.929 inches^2
Therefore, the area of the entire circle formed by the tire is approximately 530.929 square inches.
Now, we know that the decoration covers 1/9 of the circle. To find the area of the decoration, we can multiply the area of the entire circle by 1/9.
Area of decoration = (1/9) * 530.929 inches^2
≈ 58.992 inches^2
Therefore, the area of the decoration is approximately 58.992 square inches.