To find the volume of the composite figure, we need to calculate the volume of both the rectangular prism and the cube, and then add those volumes together.
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Volume of the cube: The formula for the volume of a cube is: \[ V = s^3 \] where \( s \) is the length of a side of the cube. For this cube: \[ s = 3 \text{ inches} \] Thus, the volume of the cube is: \[ V = 3^3 = 27 \text{ cubic inches} \]
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Volume of the rectangular prism: The formula for the volume of a rectangular prism is: \[ V = l \times w \times h \] where \( l \) is the length, \( w \) is the width, and \( h \) is the height. We are given:
- \( l = 11 \text{ inches} \)
- \( h = 4 \text{ inches} \)
However, we do not have the width.
Since the width of the rectangular prism is not provided in your question, if we assume the width is \( w \), then the volume of the rectangular prism is: \[ V = 11 \times w \times 4 = 44w \text{ cubic inches} \]
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Total volume of the composite figure: Assuming \( w \) is known or can be taken into consideration, the total volume \( V_t \) of the composite figure is: \[ V_t = \text{Volume of the cube} + \text{Volume of the rectangular prism} \] \[ V_t = 27 + 44w \]
If you provide the width \( w \), you can substitute that value in to find the total volume. If the width is not specified, the total volume remains as \( 27 + 44w \) cubic inches.