To find 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 area of the outer circle:
- The outer diameter is 22 inches, so the radius \( r_{\text{outer}} \) is \( \frac{22}{2} = 11 \) inches.
- The area \( A_{\text{outer}} \) is given by the formula: \[ A_{\text{outer}} = \pi r_{\text{outer}}^2 = \pi (11)^2 = 121\pi \]
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Calculate the area of the inner circle:
- The inner diameter is 18 inches, so the radius \( r_{\text{inner}} \) is \( \frac{18}{2} = 9 \) inches.
- The area \( A_{\text{inner}} \) is given by the formula: \[ A_{\text{inner}} = \pi r_{\text{inner}}^2 = \pi (9)^2 = 81\pi \]
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Calculate the area of the wreath:
- The area of the wreath \( A_{\text{wreath}} \) is the area of the outer circle minus the area of the inner circle: \[ A_{\text{wreath}} = A_{\text{outer}} - A_{\text{inner}} = 121\pi - 81\pi = 40\pi \]
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Calculating the maximum area numerically:
- Using \( \pi \approx 3.14 \): \[ A_{\text{wreath}} \approx 40 \times 3.14 = 125.6 \text{ in}^2 \]
Thus, the maximum area that Shavonne can cover with decorations is approximately 125.66 in².
The correct response is 125.66 in.².