To find the volume of the composite figure made up of the rectangular prism and the cube, we will calculate the volume of each shape separately and then add them together.
-
Volume of the rectangular prism: The formula for the volume \( V \) of a rectangular prism is given by: \[ V = \text{length} \times \text{width} \times \text{height} \] Given the dimensions:
- Length = 6 inches
- Width = 6 inches
- Height = 2 inches
Substituting the values: \[ V_{prism} = 6 , \text{in} \times 6 , \text{in} \times 2 , \text{in} = 72 , \text{in}^3 \]
-
Volume of the cube: The formula for the volume \( V \) of a cube is given by: \[ V = \text{side}^3 \] Given the side length:
- Side = 2 inches
Substituting the value: \[ V_{cube} = 2 , \text{in} \times 2 , \text{in} \times 2 , \text{in} = 8 , \text{in}^3 \]
-
Total volume of the composite figure: Now, we add the volumes of the rectangular prism and the cube: \[ V_{total} = V_{prism} + V_{cube} = 72 , \text{in}^3 + 8 , \text{in}^3 = 80 , \text{in}^3 \]
Thus, the volume of the composite figure is \( \boxed{80} , \text{in}^3 \).