To find the volume of the composite figure that consists of two cubes and a cuboid, we can follow these steps:
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Volume of the cubes: Each cube has a side length of 2 yards. The formula for the volume of a cube is: \[ V = s^3 \] where \(s\) is the length of a side.
For one cube: \[ V_{\text{cube}} = 2^3 = 8 \text{ cubic yards} \]
Since there are two cubes: \[ V_{\text{2 cubes}} = 2 \times 8 = 16 \text{ cubic yards} \]
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Volume of the cuboid: The cuboid has a length of 4.5 yards, and its width and height are the same as the sides of the cubes (2 yards).
The volume of the cuboid is given by the formula: \[ V = l \times w \times h \] where \(l\) is the length, \(w\) is the width, and \(h\) is the height.
For the cuboid: \[ V_{\text{cuboid}} = 4.5 \times 2 \times 2 \] \[ V_{\text{cuboid}} = 4.5 \times 4 = 18 \text{ cubic yards} \]
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Total Volume of the composite figure: Finally, we add the volumes of the cubes and the cuboid together: \[ V_{\text{total}} = V_{\text{2 cubes}} + V_{\text{cuboid}} \] \[ V_{\text{total}} = 16 + 18 = 34 \text{ cubic yards} \]
Thus, the volume of the composite figure is \(34 \text{ yd}^3\).