To find the volume of a square pyramid, you can use the formula:
\[ V = \frac{1}{3} \times \text{Base Area} \times \text{Height} \]
In this case, the base area of the pyramid is a square with side length of 2.75 inches. Thus, the area of the base is:
\[ \text{Base Area} = \text{side}^2 = 2.75 \times 2.75 = 7.5625 , \text{in}^2 \]
The height of the pyramid is also given as 2.75 inches.
Now, plug these values into the volume formula:
\[ V = \frac{1}{3} \times 7.5625 \times 2.75 \]
Calculating this step-by-step:
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Multiply the base area by the height: \[ 7.5625 \times 2.75 \approx 20.80 \]
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Now divide by 3 to get the volume: \[ V = \frac{20.80}{3} \approx 6.9333 \]
Rounding to the nearest hundredth gives:
\[ V \approx 6.93 , \text{in}^3 \]
Thus, the answer is:
6.93 in.³