To find the volume of the bench, we need to calculate the volume of the rectangular prism (the bench part) and the two cubes on top.
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Volume of the Cubes: Each cube has a side length of 4 inches. The volume \( V \) of a cube is calculated using the formula: \[ V = \text{side}^3 \] So, for one cube: \[ V = 4^3 = 64 \text{ cubic inches} \] Since there are two cubes, the total volume for the cubes is: \[ \text{Total volume of cubes} = 64 \text{ in}^3 \times 2 = 128 \text{ cubic inches} \]
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Height of Rectangular Prism (Bench Part): The total height of the bench is 8 inches. The height contributed by the two cubes is: \[ \text{Height of two cubes} = 4 \text{ in} (from one cube) + 4 \text{ in} (from the second cube) = 8 \text{ inches} \] Since the height of the cubes equals the total height of the bench, there is no height left for the rectangular prism (the bench part).
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Thus, Volume of the Rectangular Prism: The volume of the rectangular prism (bench part) can be calculated using: \[ \text{Volume} = \text{width} \times \text{length} \times \text{height} \] where:
- Width = 25 inches
- Length = 25 inches (since it is a rectangular bench, we assume length = width here)
- Height = 0 inches (because the height of the rectangular prism is entirely taken up by the cubes)
Therefore: \[ \text{Volume of the Rectangular Prism} = 25 \times 25 \times 0 = 0 \text{ cubic inches} \]
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Total Volume of the Bench: \[ \text{Total Volume} = \text{Volume of cubes} + \text{Volume of rectangular prism} = 128 + 0 = 128 \text{ cubic inches} \]
However, because this doesn't match any of the answer options, let's verify the dimensions given.
If we assume the bench was actually designed to have some height as a rectangular prism without being impacted by the two cubes, we might need to assume that the bench height (prism) has some measurable proportion once put back onto the height to align with similar practical designs.
But with the numbers you provided:
- Considering height given accounts for cubes entirely,
- Thus, if indeed no height can be derived for rectangular prism, checks must revert around the values/numbers given.
We'd encourage you to check back, as additional clarifications or corrections in dimensions or specifics could amend total reachable volume properly.
If considering a similar dimensional addition as suggested in other choices or to match them, check if designs differ, as numerical fixes could strongly refine outputs. Thus from given numbers, all derived volumes were prescriptive through basic calculations.
Would you like any further manipulations or formula adjustments post-check?
1 answer