An illustration shows a rectangular prism with a cube placed on top. The cube is 3 inches on all sides. The rectangular prism is 11 inches long and 4 inches high.

What is the volume of the composite figure?

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1 answer

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.

  1. 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: \[ V = 3^3 = 27 \text{ cubic inches} \]

  2. 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: \[ V = 11 \times w \times 4 = 44w \text{ cubic inches} \]

  3. 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.