To find the volume of a square pyramid, you can use the formula:
\[ \text{Volume} = \frac{1}{3} \times \text{Base Area} \times \text{Height} \]
In this case, the base of the pyramid is a square with dimensions \(2.75 , \text{in} \times 2.75 , \text{in}\).
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First, calculate the area of the base: \[ \text{Base Area} = \text{side}^2 = (2.75 , \text{in})^2 = 7.5625 , \text{in}^2 \]
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Now, use the height, which is also \(2.75 , \text{in}\): \[ \text{Height} = 2.75 , \text{in} \]
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Substitute the values into the volume formula: \[ \text{Volume} = \frac{1}{3} \times 7.5625 , \text{in}^2 \times 2.75 , \text{in} \]
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Calculate the volume: \[ \text{Volume} = \frac{1}{3} \times 7.5625 \times 2.75 = \frac{1}{3} \times 20.80 = 6.9333 , \text{in}^3 \]
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Finally, rounding to the nearest hundredth: \[ \text{Volume} \approx 6.93 , \text{in}^3 \]
Thus, the approximate volume of the ornament is 6.93 in.³.