To determine the maximum area of the wreath that Shavonne can cover with decorations, we need to calculate the area of the outer circle and subtract the area of the inner circle.
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Calculate the radius of the outer circle:
- Outer diameter = 22 in, so outer radius \( R = \frac{22}{2} = 11 \) in.
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Calculate the radius of the inner circle:
- Inner diameter = 18 in, so inner radius \( r = \frac{18}{2} = 9 \) in.
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Calculate the area of the outer circle: \[ \text{Area}_{\text{outer}} = \pi R^2 = \pi (11)^2 = 121\pi \text{ in}^2 \]
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Calculate the area of the inner circle: \[ \text{Area}_{\text{inner}} = \pi r^2 = \pi (9)^2 = 81\pi \text{ in}^2 \]
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Calculate the area of the wreath: \[ \text{Area}{\text{wreath}} = \text{Area}{\text{outer}} - \text{Area}_{\text{inner}} = 121\pi - 81\pi = 40\pi \text{ in}^2 \]
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Calculate a numerical value:
- Using \( \pi \approx 3.14 \): \[ \text{Area}_{\text{wreath}} \approx 40 \times 3.14 = 125.6 \text{ in}^2 \]
Thus, the maximum area of the wreath that Shavonne can cover with decorations is approximately 125.66 in².
The correct answer is: 125.66 in.²