A cuboid is of measure 64 cm x 54 cm x 30 cm. How many small cubes with sides 6 cm can be placed in the given cuboid ?

Question

Accepted Answer

To determine how many small cubes with sides of 6 cm can be placed in the given cuboid with dimensions 64 cm x 54 cm x 30 cm, we need to calculate the volume of both the cuboid and the small cubes, and then see how many small cubes fit into the cuboid.

1. **Calculate the volume of the cuboid:**
   - The volume of a cuboid is given by the formula: Volume = length × width × height.
   - For the given cuboid: Volume = 64 cm × 54 cm × 30 cm = 103,680 cubic centimeters.

2. **Calculate the volume of a small cube:**
   - The volume of a cube is given by the formula: Volume = side³.
   - For the small cube with side 6 cm: Volume = 6 cm × 6 cm × 6 cm = 216 cubic centimeters.

3. **Determine how many small cubes fit into the cuboid:**
   - To find the number of small cubes that can fit into the cuboid, divide the volume of the cuboid by the volume of one small cube.
   - Number of small cubes = Volume of cuboid / Volume of one small cube = 103,680 / 216 = 480.

Therefore, 480 small cubes with sides of 6 cm can be placed in the given cuboid. This calculation confirms that Option 2 is correct.

**Explanation for why other options are incorrect:**

- **Option 1 (380):** This option is incorrect because the calculation shows that 480 small cubes fit into the cuboid, not 380. The division of the cuboid's volume by the volume of a small cube results in 480, not 380.

- **Option 3 (520):** This option is incorrect because it exceeds the actual number of small cubes that can fit into the cuboid. The correct calculation yields 480, not 520.

- **Option 4 (525):** This option is incorrect for the same reason as Option 3. The calculation clearly shows that only 480 small cubes can fit, not 525.

In conclusion, the correct answer is Option 2, as the calculation accurately supports that 480 small cubes can be placed in the given cuboid.