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Seven cubes each of sides 4 cm are joined end to end. The volume of the resulting cuboid would be
- a)520 cm3
- b)480 cm3
- c)448 cm3
- d)400 cm3
Correct answer is option 'C'. Can you explain this answer?
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Understanding the Problem
To find the volume of the resulting cuboid formed by joining seven cubes, we first need to determine the dimensions of the cuboid.
Dimensions of a Single Cube
- Each cube has a side length of 4 cm.
- Volume of a single cube = side × side × side = 4 cm × 4 cm × 4 cm = 64 cm³.
Joining the Cubes
- When seven cubes are joined end to end, the length of the resulting cuboid will be the combined lengths of the cubes.
- Total length = 7 cubes × 4 cm = 28 cm.
- The other two dimensions (width and height) remain the same as the cube's dimensions, which are both 4 cm.
Calculating the Volume of the Cuboid
- Volume of the cuboid = length × width × height.
- Thus, Volume = 28 cm × 4 cm × 4 cm.
Performing the Calculation
- Volume = 28 × 4 × 4 = 448 cm³.
Conclusion
The volume of the resulting cuboid formed by joining seven cubes each of side 4 cm is 448 cm³. Therefore, the correct answer is option 'C'.
To find the volume of the resulting cuboid formed by joining seven cubes, we first need to determine the dimensions of the cuboid.
Dimensions of a Single Cube
- Each cube has a side length of 4 cm.
- Volume of a single cube = side × side × side = 4 cm × 4 cm × 4 cm = 64 cm³.
Joining the Cubes
- When seven cubes are joined end to end, the length of the resulting cuboid will be the combined lengths of the cubes.
- Total length = 7 cubes × 4 cm = 28 cm.
- The other two dimensions (width and height) remain the same as the cube's dimensions, which are both 4 cm.
Calculating the Volume of the Cuboid
- Volume of the cuboid = length × width × height.
- Thus, Volume = 28 cm × 4 cm × 4 cm.
Performing the Calculation
- Volume = 28 × 4 × 4 = 448 cm³.
Conclusion
The volume of the resulting cuboid formed by joining seven cubes each of side 4 cm is 448 cm³. Therefore, the correct answer is option 'C'.
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Seven cubes each of sides 4 cm are joined end to end. The volume of the resulting cuboid would bea)520 cm3b)480 cm3c)448 cm3d)400 cm3Correct answer is option 'C'. Can you explain this answer?
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