The length, breadth and height of a solid cuboid is 14 cm, 12 cm and 8 cm respectively. If cuboid is melted to form identical cubes of side 2 cm, then what will be the number of identical cubes?

Options

A. 168
B. 144
C. 156
D. 128

Answer

To solve the problem step by step, we will calculate the volume of the cuboid and then determine how many identical cubes can be formed from that volume.

### Step 1: Calculate the Volume of the Cuboid
The volume \( V \) of a cuboid is given by the formula:
\[ V = \text{length} \times \text{breadth} \times \text{height} \]
Given:
- Length = 14 cm
- Breadth = 12 cm
- Height = 8 cm

Substituting the values:
\[ V = 14 \times 12 \times 8 \]

### Step 2: Perform the Multiplication
Calculating the volume:
\[ 14 \times 12 = 168 \]
Now, multiply this result by the height:
\[ 168 \times 8 = 1344 \text{ cm}^3 \]
So, the volume of the cuboid is \( 1344 \text{ cm}^3 \).

### Step 3: Calculate the Volume of One Cube
The volume \( V_c \) of a cube is given by the formula:
\[ V_c = \text{side}^3 \]
Given that the side of the cube is 2 cm:
\[ V_c = 2 \times 2 \times 2 = 8 \text{ cm}^3 \]

### Step 4: Determine the Number of Identical Cubes
Let \( n \) be the number of identical cubes formed. The total volume of the cubes will equal the volume of the cuboid:
\[ n \times V_c = V \]
Substituting the known volumes:
\[ n \times 8 = 1344 \]

### Step 5: Solve for \( n \)
To find \( n \):
\[ n = \frac{1344}{8} \]
Calculating this gives:
\[ n = 168 \]

### Conclusion
The number of identical cubes formed from melting the cuboid is **168**.