To calculate the volume of the triangular prism container, we need to first determine the area of the triangular base and then multiply it by the length of the prism.
Step 1: Calculate the area of the triangular base
The triangular base has a width (base) of 9 inches and a height of 3 inches. The area \( A \) of a triangle is given by the formula:
\[ A = \frac{1}{2} \times \text{base} \times \text{height} \]
Substituting the given values:
\[ A = \frac{1}{2} \times 9 , \text{in} \times 3 , \text{in} = \frac{1}{2} \times 27 , \text{in}^2 = 13.5 , \text{in}^2 \]
Step 2: Calculate the volume of the prism
The volume \( V \) of a prism is given by the formula:
\[ V = \text{Base Area} \times \text{Length} \]
The length of the prism is given as 12 inches. Now substituting the area we calculated:
\[ V = 13.5 , \text{in}^2 \times 12 , \text{in} = 162 , \text{in}^3 \]
Conclusion
The volume of the container is \( 162 , \text{in}^3 \).
None of the given options (A, B, C, D) match this calculated volume, suggesting either the parameters need to be re-evaluated or the options provided don't correspond accurately to the volume calculated. The options provided appear to be for square inches rather than cubic inches as well, which might also indicate a misinterpretation of the problem.