The volume \( V \) of a square pyramid can be calculated using the formula:
\[ V = \frac{1}{3} \times \text{base area} \times \text{height} \]
For a square pyramid, the base area is given by the square of the length of one side of the base. In this case, since the base is a square with dimensions 2.75 in by 2.75 in, we can calculate the base area as follows:
\[ \text{base area} = \text{side}^2 = (2.75 \text{ in})^2 = 7.5625 \text{ in}^2 \]
The height of the pyramid is also given as 2.75 in.
Now substituting these values into the volume formula:
\[ V = \frac{1}{3} \times 7.5625 \text{ in}^2 \times 2.75 \text{ in} \]
Calculating the volume:
\[ V = \frac{1}{3} \times 7.5625 \times 2.75 \] \[ = \frac{1}{3} \times 20.80 \] \[ = 6.9333\ldots \text{ in}^3 \]
Rounded to the nearest hundredth, the volume of the ornament is approximately:
\[ \boxed{6.93} \text{ in}^3 \]