To find the volume of the composite figure consisting of a cube on top of a rectangular prism, we need to calculate the volumes of both the cube and the rectangular prism separately, and then sum them.
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Volume of the rectangular prism: The formula for the volume \(V\) of a rectangular prism is: \[ V = \text{length} \times \text{width} \times \text{height} \] Given:
- Length = 6 inches
- Width = 6 inches (assuming width is the same as length)
- Height = 2 inches
Now, calculate the volume: \[ V_{prism} = 6 , \text{in} \times 6 , \text{in} \times 2 , \text{in} = 72 , \text{in}^3 \]
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Volume of the cube: The formula for the volume \(V\) of a cube is: \[ V = \text{side}^3 \] Given:
- Side length = 2 inches
Now, calculate the volume: \[ V_{cube} = 2 , \text{in} \times 2 , \text{in} \times 2 , \text{in} = 8 , \text{in}^3 \]
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Total volume of the composite figure: Now, add the volumes of the prism and the cube: \[ V_{total} = V_{prism} + V_{cube} = 72 , \text{in}^3 + 8 , \text{in}^3 = 80 , \text{in}^3 \]
Therefore, the volume of the composite figure is 80 in³.