Question

This figure is made up of two rectangular prisms.

What is the volume of the figure?

Enter your answer in the box.

ft³
Three-dimensional figure that could be formed by placing a smaller rectangular prism on top of a larger rectangular prism such that the widths of the prisms are the same. The larger bottom prism has a length of 19 feet, a width of 12 feet, and a height of 6 feet. The smaller top prism has a length of 10 feet and a height of 3 feet.

Answer 1

To find the volume of the figure made up of two rectangular prisms, we need to calculate the volume of each prism separately and then add them together.

1. **Volume of the larger rectangular prism**:
- **Length** = 19 feet
- **Width** = 12 feet
- **Height** = 6 feet

Volume of a rectangular prism is calculated using the formula:
\[
V = \text{Length} \times \text{Width} \times \text{Height}
\]
Substituting the dimensions of the larger prism:
\[
V = 19 \times 12 \times 6
\]
\[
V = 228 \times 6 = 1368 \text{ ft}^3
\]

2. **Volume of the smaller rectangular prism**:
- **Length** = 10 feet
- **Width** = 12 feet (same as the larger prism since they share the same width)
- **Height** = 3 feet

Using the same volume formula for the smaller prism:
\[
V = \text{Length} \times \text{Width} \times \text{Height}
\]
Substituting the dimensions of the smaller prism:
\[
V = 10 \times 12 \times 3
\]
\[
V = 120 \times 3 = 360 \text{ ft}^3
\]

3. **Total volume of the figure**:
Now, we add the volumes of both prisms:
\[
\text{Total Volume} = \text{Volume of larger prism} + \text{Volume of smaller prism}
\]
\[
\text{Total Volume} = 1368 + 360 = 1728 \text{ ft}^3
\]

Thus, the total volume of the figure is:
\[
\boxed{1728} \text{ ft}^3
\]