The length, breadth andheight of a solid cuboid is 20 cm, 16 cm and 12 cm respectively. If cuboid is melted to form identical cubes of side 4 cm, then what will be the number of identical cubes?

Options

A. 56
B. 72
C. 90
D. 60

Answer

To find the number of identical cubes that can be formed from a solid cuboid, we need to follow these steps:

### Step 1: Calculate the Volume of the Cuboid
The volume \( V \) of a cuboid can be calculated using the formula:
\[ V = \text{length} \times \text{breadth} \times \text{height} \]
Given:
- Length = 20 cm
- Breadth = 16 cm
- Height = 12 cm

Substituting the values:
\[ V = 20 \, \text{cm} \times 16 \, \text{cm} \times 12 \, \text{cm} \]

### Step 2: Perform the Multiplication
Now, we will calculate the volume:
\[ V = 20 \times 16 = 320 \, \text{cm}^2 \]
Then,
\[ V = 320 \times 12 = 3840 \, \text{cm}^3 \]

### Step 3: Calculate the Volume of One Cube
The volume \( V_c \) of a cube can be calculated using the formula:
\[ V_c = \text{side}^3 \]
Given:
- Side of the cube = 4 cm

Substituting the value:
\[ V_c = 4 \, \text{cm} \times 4 \, \text{cm} \times 4 \, \text{cm} = 64 \, \text{cm}^3 \]

### Step 4: Calculate the Number of Identical Cubes
To find the number of identical cubes, we divide the volume of the cuboid by the volume of one cube:
\[ \text{Number of cubes} = \frac{V}{V_c} = \frac{3840 \, \text{cm}^3}{64 \, \text{cm}^3} \]

### Step 5: Perform the Division
Calculating the number of cubes:
\[ \text{Number of cubes} = \frac{3840}{64} = 60 \]

### Final Answer
The number of identical cubes that can be formed is **60**.

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