Question

Find the volume of this composite figure.



Volume of Right Prism or Cylinder = (area of base)(height) or V = Bh

(4 points)
Volume of the left cube =
cubic centimeters

Volume of the middle rectangular prism =
cubic centimeters

Volume of the right cube =
cubic centimeters

Volume of the entire composite figure =
cubic centimeters

answer

Answer 1

To find the volume of the composite figure consisting of two cubes and one rectangular prism, we need the dimensions of each part to calculate their volumes using the appropriate formulas.

1. **Volume of the left cube**:
- If the side length of the cube is \( s \), then the volume \( V \) of a cube is given by:
\[
V = s^3
\]

2. **Volume of the middle rectangular prism**:
- If the dimensions of the rectangular prism are \( l \) (length), \( w \) (width), and \( h \) (height), then the volume \( V \) is given by:
\[
V = l \times w \times h
\]

3. **Volume of the right cube**:
- If the side length of the cube is \( s' \), then the volume \( V \) of this cube is also:
\[
V = {s'}^3
\]

4. **Volume of the entire composite figure**:
- The total volume \( V \) is the sum of the volumes of all parts:
\[
V_{\text{total}} = V_{\text{left cube}} + V_{\text{middle rectangular prism}} + V_{\text{right cube}}
\]

### Sample Calculation:
Assuming we have specific side lengths and dimensions, plug those values into the formulas above.

Let’s say:
- Left cube side = 3 cm -> Volume = \( 3^3 = 27 \) cm³
- Rectangular prism dimensions (length = 4 cm, width = 5 cm, height = 6 cm) -> Volume = \( 4 \times 5 \times 6 = 120 \) cm³
- Right cube side = 2 cm -> Volume = \( 2^3 = 8 \) cm³

Now calculate the total volume:
\[
V_{\text{total}} = 27 + 120 + 8 = 155 \text{ cm}^3
\]

### Answer Formatting:
1. Volume of the left cube = **27** cubic centimeters
2. Volume of the middle rectangular prism = **120** cubic centimeters
3. Volume of the right cube = **8** cubic centimeters
4. Volume of the entire composite figure = **155** cubic centimeters

Please provide the specific measurements for accurate volume calculation if not covered in this example!