To find the volume of a square pyramid, you can use the formula:
\[ V = \frac{1}{3} \times \text{Base Area} \times \text{Height} \]
For a square pyramid with a base side length of \( s \) and a height \( h \):
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Calculate the base area (which is a square): \[ \text{Base Area} = s^2 \] Since the dimensions given are 2.75 inches, we have: \[ \text{Base Area} = (2.75)^2 = 7.5625 , \text{in}^2 \]
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The height of the pyramid is also 2.75 inches.
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Now, plug these values into the volume formula: \[ V = \frac{1}{3} \times 7.5625 \times 2.75 \]
Calculating this:
First, multiply the base area by the height: \[ 7.5625 \times 2.75 = 20.80 , \text{in}^3 \]
Now, divide by 3 to get the volume: \[ V = \frac{20.80}{3} \approx 6.9333 , \text{in}^3 \]
Rounding to the nearest hundredth, the volume is: \[ \approx 6.93 , \text{in}^3 \]
Thus, the approximate volume of the ornament is 6.93 in.³.