To calculate the area of the wreath that Brianna can decorate, we first need to determine 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:
- The outer diameter is 18 inches, so the radius \( r_{outer} \) is: \[ r_{outer} = \frac{18}{2} = 9 \text{ inches} \]
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Calculate the radius of the inner circle:
- The inner diameter is 12 inches, so the radius \( r_{inner} \) is: \[ r_{inner} = \frac{12}{2} = 6 \text{ inches} \]
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Calculate the area of the outer circle: \[ A_{outer} = \pi r_{outer}^2 = \pi (9)^2 = 81\pi \text{ square inches} \]
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Calculate the area of the inner circle: \[ A_{inner} = \pi r_{inner}^2 = \pi (6)^2 = 36\pi \text{ square inches} \]
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Calculate the area of the wreath: \[ A_{wreath} = A_{outer} - A_{inner} = 81\pi - 36\pi = 45\pi \text{ square inches} \]
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Calculate the area in decimal form using \( \pi \approx 3.14 \): \[ A_{wreath} \approx 45 \times 3.14 \approx 141.3 \text{ square inches} \]
Thus, the maximum area of the wreath that Brianna can cover with decorations is approximately \( 141.37 \) square inches.
The correct response is: 141.37 square inches