To find the volume of a right rectangular pyramid, we can use the formula:
\[ V = \frac{1}{3} \times B \times h \]
where \(B\) is the area of the base and \(h\) is the height of the pyramid.
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Calculate the area of the base: The base of the pyramid is a rectangle. The area \(B\) can be calculated using the formula:
\[ B = \text{length} \times \text{width} \] Given the length \(l = 6.75\) inches and the width \(w = 10.25\) inches:
\[ B = 6.75 \times 10.25 = 69.1875 \text{ square inches} \]
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Calculate the volume: Now we can substitute \(B\) and the height \(h = 22.3\) inches into the volume formula:
\[ V = \frac{1}{3} \times 69.1875 \times 22.3 \]
First, calculate \(69.1875 \times 22.3\):
\[ 69.1875 \times 22.3 = 1545.68725 \]
Now, divide by 3 to find the volume:
\[ V = \frac{1545.68725}{3} = 515.2290833 \]
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Round to the nearest hundredth: Rounding \(515.2290833\) to the nearest hundredth gives:
\[ 515.23 \]
Thus, the volume of the pyramid is \(\boxed{515.23}\) cubic inches.