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

Options

A. A)380
B. B)480
C. C)520
D. D)525

Answer

To determine how many small cubes with a side of 6 cm can fit into a cuboid measuring 64 cm x 54 cm x 30 cm, we can follow these steps:

### Step 1: Calculate the volume of the cuboid.
The volume \( V \) of a cuboid can be calculated using the formula:
\[ V = \text{length} \times \text{width} \times \text{height} \]
Substituting the given dimensions:
\[ V = 64 \, \text{cm} \times 54 \, \text{cm} \times 30 \, \text{cm} \]

### Step 2: Calculate the volume of one small cube.
The volume \( v \) of a cube can be calculated using the formula:
\[ v = \text{side}^3 \]
For a cube with a side of 6 cm:
\[ v = 6 \, \text{cm} \times 6 \, \text{cm} \times 6 \, \text{cm} = 216 \, \text{cm}^3 \]

### Step 3: Calculate the total number of small cubes that can fit in the cuboid.
To find the number of small cubes that can fit in the cuboid, we divide the volume of the cuboid by the volume of one small cube:
\[ \text{Number of cubes} = \frac{\text{Volume of cuboid}}{\text{Volume of one small cube}} = \frac{64 \times 54 \times 30}{216} \]

### Step 4: Simplify the calculation.
First, calculate the volume of the cuboid:
\[ 64 \times 54 = 3456 \]
\[ 3456 \times 30 = 103680 \, \text{cm}^3 \]
Now, divide by the volume of one small cube:
\[ \text{Number of cubes} = \frac{103680}{216} \]

### Step 5: Perform the division.
Calculating the division:
\[ \frac{103680}{216} = 480 \]

### Conclusion:
Thus, the total number of small cubes that can be placed in the given cuboid is **480**.

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