To find the volume \( V \) of a right rectangular pyramid, we use the formula:
\[ V = \frac{1}{3} \times \text{Base Area} \times \text{Height} \]
First, we need to calculate the base area. Since the base is a rectangle, we can find the area \( A \) using the length and width:
\[ A = \text{length} \times \text{width} = 6.75 , \text{inches} \times 10.25 , \text{inches} \]
Calculating the base area:
\[ A = 6.75 \times 10.25 = 69.1875 , \text{square inches} \]
Next, we need to use the altitude (height) of the pyramid, which is given as 22.3 inches, to find the volume:
\[ V = \frac{1}{3} \times 69.1875 , \text{inches}^2 \times 22.3 , \text{inches} \]
Calculating the volume step-by-step:
- Calculate \( 69.1875 \times 22.3 \):
\[ 69.1875 \times 22.3 = 1546.6875 , \text{cubic inches} \]
- Now multiply by \(\frac{1}{3}\):
\[ V = \frac{1546.6875}{3} = 515.5625 , \text{cubic inches} \]
Finally, we round the volume to the nearest hundredth:
\[ V \approx 515.56 , \text{cubic inches} \]
Thus, the volume of the pyramid is
\[ \boxed{515.56} , \text{cubic inches} \]