Question

A slice of pizza is held in a container shaped like a triangular prism. The dimensions of the container are described below.
Width 9 in.
Height 3 in
length 12 in
length of top connecting to bottom 7 in
what is the volume of the container in cubic inches

Answer 1

To find the volume of the triangular prism-shaped container, we need to use the formula for the volume of a prism, which is:

\[
\text{Volume} = \text{Base Area} \times \text{Height}
\]

1. **Identify the base of the prism**: In this case, the base is a triangle. The problem gives us the width and the height of the triangle, which are the two dimensions needed to calculate the area of the triangular base.

- Width (base of the triangle) = 9 inches
- Height of the triangle = 3 inches

2. **Calculate the area of the triangular base**:

\[
\text{Area of the triangle} = \frac{1}{2} \times \text{base} \times \text{height} = \frac{1}{2} \times 9 \, \text{in} \times 3 \, \text{in} = \frac{1}{2} \times 27 \, \text{in}^2 = 13.5 \, \text{in}^2
\]

3. **Now find the volume**: With the area of the base calculated, we'll multiply it by the length of the prism to get the volume.

- Length of the prism = 12 inches

\[
\text{Volume} = \text{Base Area} \times \text{Length} = 13.5 \, \text{in}^2 \times 12 \, \text{in} = 162 \, \text{in}^3
\]

Thus, the volume of the container is

\[
\boxed{162 \, \text{cubic inches}}
\]