To find the volume of a rectangular pyramid, you can use the formula:
\[ V = \frac{1}{3} \times \text{Base Area} \times \text{Height} \]
Given:
- Length of the base (l) = 10 dm
- Width of the base (w) = 4 dm
- Height of the pyramid (h) = 10 dm
First, calculate the base area:
\[ \text{Base Area} = \text{Length} \times \text{Width} = 10 , \text{dm} \times 4 , \text{dm} = 40 , \text{dm}^2 \]
Now, plug the base area and height into the volume formula:
\[ V = \frac{1}{3} \times 40 , \text{dm}^2 \times 10 , \text{dm} \] \[ V = \frac{1}{3} \times 400 , \text{dm}^3 \] \[ V = \frac{400}{3} , \text{dm}^3 \approx 133.33 , \text{dm}^3 \]
Rounded to the nearest hundredth, the volume of the pyramid is:
133.33 dm³.