To find the volume of a rectangular pyramid, we use the formula:
\[ \text{Volume} = \frac{1}{3} \times \text{Base Area} \times \text{Height} \]
In this case, the base of the pyramid is a rectangle with dimensions of length (14 inches) and width (6 inches). First, we calculate the area of the base:
\[ \text{Base Area} = \text{Length} \times \text{Width} = 14 , \text{inches} \times 6 , \text{inches} = 84 , \text{square inches} \]
Next, we have the height of the pyramid, which is given as 12 inches.
Now we can calculate the volume:
\[ \text{Volume} = \frac{1}{3} \times 84 , \text{in}^2 \times 12 , \text{in} \]
Calculating the volume step-by-step:
- Calculate \(84 \times 12\):
\[ 84 \times 12 = 1008 , \text{cubic inches} \]
- Now take \(\frac{1}{3}\) of 1008:
\[ \text{Volume} = \frac{1008}{3} = 336 , \text{cubic inches} \]
Thus, the volume of the rectangular pyramid is \(336 , \text{in}^3\).
So the correct answer is:
336 in.³