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