The volume \( V \) of a rectangular pyramid can be calculated using the formula:
\[ V = \frac{1}{3} \times \text{Base Area} \times \text{Height} \]
For a rectangular base, the base area \( A \) is given by:
\[ A = \text{length} \times \text{width} \]
In this case, the base dimensions are 3 inches and 4 inches:
\[ A = 3 , \text{in} \times 4 , \text{in} = 12 , \text{in}^2 \]
The height (altitude) of the pyramid is 6 inches. Now, we can substitute the values into the volume formula:
\[ V = \frac{1}{3} \times 12 , \text{in}^2 \times 6 , \text{in} \]
Now, calculate it step-by-step:
-
Calculate the area times the height: \[ 12 , \text{in}^2 \times 6 , \text{in} = 72 , \text{in}^3 \]
-
Now, calculate the volume: \[ V = \frac{1}{3} \times 72 , \text{in}^3 = 24 , \text{in}^3 \]
Thus, the volume of the rectangular pyramid is:
\[ \boxed{24 , \text{in}^3} \]