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.
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Volume of the left cube:
- If the side length of the cube is \( s \), then the volume \( V \) of a cube is given by: \[ V = s^3 \]
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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: \[ V = l \times w \times h \]
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Volume of the right cube:
- If the side length of the cube is \( s' \), then the volume \( V \) of this cube is also: \[ V = {s'}^3 \]
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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:
- Volume of the left cube = 27 cubic centimeters
- Volume of the middle rectangular prism = 120 cubic centimeters
- Volume of the right cube = 8 cubic centimeters
- Volume of the entire composite figure = 155 cubic centimeters
Please provide the specific measurements for accurate volume calculation if not covered in this example!