To find the volume of the composite figure, we need to calculate the volume of both the rectangular prism and the cube, then add them together.
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Volume of the cube: The formula for the volume of a cube is given by: \[ V = s^3 \] where \( s \) is the length of a side. Given that the sides of the cube are 3 feet: \[ V_{\text{cube}} = 3^3 = 27 \text{ ft}^3 \]
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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. For the prism, given that its length and width are both 1 foot and its height is 3 feet: \[ V_{\text{prism}} = 1 \times 1 \times 3 = 3 \text{ ft}^3 \]
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Total volume of the composite figure: Now we can add the volumes of the cube and the prism: \[ V_{\text{total}} = V_{\text{cube}} + V_{\text{prism}} = 27 \text{ ft}^3 + 3 \text{ ft}^3 = 30 \text{ ft}^3 \]
Thus, the volume of the composite figure is 30 ft³.