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 this pyramid:
- The base dimensions are given as length \( l = 10 \) dm and width \( w = 4 \) dm.
- The height \( h = 10 \) dm.
First, calculate the area of the base:
\[ \text{Base Area} = l \times w = 10 , \text{dm} \times 4 , \text{dm} = 40 , \text{dm}^2 \]
Now, substitute the base area and height into the volume formula:
\[ V = \frac{1}{3} \times 40 , \text{dm}^2 \times 10 , \text{dm} \]
Calculating this:
\[ V = \frac{1}{3} \times 400 , \text{dm}^3 = \frac{400}{3} , \text{dm}^3 \approx 133.33 , \text{dm}^3 \]
Thus, the volume of the pyramid is approximately \( 133.33 , \text{dm}^3 \).
So the correct response is:
133.33 dm cubed.