To find the maximum area of the wreath that Shavonne can cover with decorations, we need to calculate the area of the ring that is formed between the outer diameter and the inner diameter of the wreath.
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Calculate the outer radius (R): \[ R = \frac{22 \text{ in}}{2} = 11 \text{ in} \]
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Calculate the inner radius (r): \[ r = \frac{18 \text{ in}}{2} = 9 \text{ in} \]
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Calculate the area of the entire wreath (outer circle): \[ \text{Area}_{\text{outer}} = \pi R^2 = \pi (11 \text{ in})^2 = \pi \times 121 \text{ in}^2 \approx 380.13 \text{ in}^2 \]
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Calculate the area of the inner circle: \[ \text{Area}_{\text{inner}} = \pi r^2 = \pi (9 \text{ in})^2 = \pi \times 81 \text{ in}^2 \approx 254.47 \text{ in}^2 \]
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Calculate the area of the wreath by subtracting the inner area from the outer area: \[ \text{Area}{\text{wreath}} = \text{Area}{\text{outer}} - \text{Area}_{\text{inner}} \approx 380.13 \text{ in}^2 - 254.47 \text{ in}^2 \approx 125.66 \text{ in}^2 \]
Now, the area is in square inches, but it appears from the responses that they are given in square feet. To convert from square inches to square feet: \[ \text{Area in ft}^2 = \frac{125.66 \text{ in}^2}{144} \approx 0.873 \text{ ft}^2 \]
However, this conversion shows that I must verify the context of your question since the options listed are much larger numbers.
It seems there might be confusion regarding the question or the choices provided. Based on the given measurements, you would not cover an area as large as those choices imply from the area calculations.
Based on the values, it appears possible there's a typographical error or misunderstanding. Please confirm the data provided or clarify, so I can help determine the decorable area correctly.
3 answers