Question

What is the volume of the composite figure shown below?


2 rectangular prisms. One prism has a length of 13 millimeters, width of 12 millimeters, and height of 12 millimeters. The other prism has a length of 15 millimeters, width of 12 millimeters, and height of 3 millimeters.
1,008 millimeters cubed
2,412 millimeters cubed
2,880 millimeters cubed
3,465 millimeters cubed

Answer 1

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

1. **Volume of the first rectangular prism**:
- Length = 13 mm
- Width = 12 mm
- Height = 12 mm

\[
\text{Volume}_1 = \text{Length} \times \text{Width} \times \text{Height} = 13 \times 12 \times 12
\]

\[
\text{Volume}_1 = 13 \times 144 = 1,872 \text{ mm}^3
\]

2. **Volume of the second rectangular prism**:
- Length = 15 mm
- Width = 12 mm
- Height = 3 mm

\[
\text{Volume}_2 = \text{Length} \times \text{Width} \times \text{Height} = 15 \times 12 \times 3
\]

\[
\text{Volume}_2 = 15 \times 36 = 540 \text{ mm}^3
\]

3. **Total volume of the composite figure**:
- Now, we add the volumes of the two prisms:

\[
\text{Total Volume} = \text{Volume}_1 + \text{Volume}_2 = 1,872 + 540
\]

\[
\text{Total Volume} = 2,412 \text{ mm}^3
\]

Thus, the volume of the composite figure is **2,412 millimeters cubed**.