Question

Juan builds this pedestal for a trophy.

What is the volume of the pedestal?

Enter your answer in the box.

in³
Three-dimensional figure that could be formed by putting 2 rectangular prisms together. The front of the solid forms an upside-down T. The bottom prism is 9 inches long, 2 inches wide, and 4 inches high. The top prism is 4 inches high. The top of the bottom prism measures 2 inches from the right edge to where it meets the top prism. It also measures 2 inches from the left edge to where it meets the top prism.

Answer 1

To find the volume of the pedestal, we need to calculate the volume of both rectangular prisms and then sum them up.

1. **Volume of the bottom prism:**
- Dimensions: Length = 9 inches, Width = 2 inches, Height = 4 inches
- Volume = Length × Width × Height
\[
\text{Volume}_{\text{bottom}} = 9 \, \text{inches} \times 2 \, \text{inches} \times 4 \, \text{inches}
\]
\[
\text{Volume}_{\text{bottom}} = 72 \, \text{in}^3
\]

2. **Volume of the top prism:**
- Dimensions: Length = 4 inches (the width of the top prism is not specified but we can see it's placed centered on top of the bottom prism), the Width = 2 inches (same width as the bottom prism), Height = 4 inches.
However, from the description, the top prism is 2 inches wide, and it also has a length of 4 inches and a height of 4 inches.
- Volume = Length × Width × Height
\[
\text{Volume}_{\text{top}} = 5 \, \text{inches} \times 2 \, \text{inches} \times 4 \, \text{inches}
\]
\[
\text{Volume}_{\text{top}} = 40 \, \text{in}^3
\]

3. **Total Volume of the pedestal:**
\[
\text{Total Volume} = \text{Volume}_{\text{bottom}} + \text{Volume}_{\text{top}}
\]
\[
\text{Total Volume} = 72 \, \text{in}^3 + 40 \, \text{in}^3
\]
\[
\text{Total Volume} = 112 \, \text{in}^3
\]

Therefore, the volume of the pedestal is \( \boxed{112} \) in³.