To find the volume of the composite figure, we need to calculate the volumes of both the rectangular prism and the cube, and then sum them.
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Volume of the Cube: The formula for the volume of a cube is: \[ V = s^3 \] where \(s\) is the side length.
For the cube with a side length of 3 inches: \[ V_{\text{cube}} = 3^3 = 27 \text{ cubic inches} \]
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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.
The dimensions given are:
- Length (\(l\)) = 11 inches
- Width (\(w\)) = (Since it isn't explicitly provided, let's assume the width is necessary for volume calculation. We will denote it as \(w\)).
- Height (\(h\)) = 4 inches
Thus, the volume of the rectangular prism can be expressed as: \[ V_{\text{prism}} = 11 \times w \times 4 \] Without the width, we cannot compute a specific volume for the prism.
Assuming we assume or find that width to be given as well or solve it through other means, we will carry on assuming \( w = 4 \) as a placeholder.
\[ V_{\text{prism}} = 11 \times 4 \times 4 = 176 \text{ cubic inches} \]
- Total Volume of the Composite Figure: Now we can sum the volumes of both the cube and the rectangular prism. \[ V_{\text{total}} = V_{\text{cube}} + V_{\text{prism}} \] Assuming \( w = 4 \): \[ V_{\text{total}} = 27 + 176 = 203 \text{ cubic inches} \]
Thus, the answer is: \[ \text{Total Volume} = 203 \text{ in}^3 \]
If any width information changes, please update it, and we will adjust the height accordingly.