Three identical solid cubes of side 2 cm each are placed one over another to form a cuboid. What is the volume of the resulting cuboid?
$24 cm^3$
To solve this problem, we must first understand the configuration and dimensions of the solid shapes involved.
We are given that we have three identical solid cubes, each with a side length of 2 cm. The cubes are placed one over another to form a cuboid.
The volume of a cube is given by the formula:
V_{\text{cube}} = a^3, where a is the side length of the cube.
Substituting the given side length of the cube, we have:
V_{\text{cube}} = (2 \, \text{cm})^3 = 8 \, \text{cm}^3
Since three cubes are stacked to form the cuboid, the dimensions of the resulting cuboid become:
- Length = 2 cm (same as the side of a cube)
- Breadth = 2 cm (same as the side of a cube)
- Height = 3 × 2 cm = 6 cm (because three cubes are stacked vertically)
Now, the volume of the cuboid is calculated using the formula:
V_{\text{cuboid}} = \text{Length} \times \text{Breadth} \times \text{Height}
Substituting the measurements:
V_{\text{cuboid}} = 2 \, \text{cm} \times 2 \, \text{cm} \times 6 \, \text{cm} = 24 \, \text{cm}^3
Therefore, the volume of the resulting cuboid is 24 \, \text{cm}^3.
Upon analysis of the options given:
- 8 \, \text{cm}^3: This is the volume of a single cube, not the cuboid.
- 16 \, \text{cm}^3: This is not correct as it doesn't account for stacking three cubes.
- 24 \, \text{cm}^3: This matches our calculated volume of the cuboid.
- 32 \, \text{cm}^3: This is incorrect based on our calculations.
Thus, the correct answer is 24 \, \text{cm}^3.
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