A solid metallic cuboid of dimensions `9m xx 8m xx2` is melted and recast in to solid cubes of edge 2 m .find the number of cubes so formed.

Explanation

To find the number of cubes formed when a solid metallic cuboid is melted and recast into solid cubes, we will 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 the dimensions of the cuboid are \( 9 \, \text{m} \times 8 \, \text{m} \times 2 \, \text{m} \), we can substitute these values into the formula:
\[ V = 9 \times 8 \times 2 \]

### Step 2: Perform the Multiplication
Now, we will perform the multiplication:
\[ V = 9 \times 8 = 72 \]
\[ V = 72 \times 2 = 144 \, \text{m}^3 \]
So, the volume of the cuboid is \( 144 \, \text{m}^3 \).

### Step 3: Calculate the Volume of One Cube
The volume \( V_c \) of a cube can be calculated using the formula:
\[ V_c = \text{Edge}^3 \]
Given the edge of the cube is \( 2 \, \text{m} \):
\[ V_c = 2^3 = 2 \times 2 \times 2 = 8 \, \text{m}^3 \]

### Step 4: Calculate the Number of Cubes
To find the number of cubes formed, we divide the volume of the cuboid by the volume of one cube:
\[ \text{Number of cubes} = \frac{\text{Volume of cuboid}}{\text{Volume of one cube}} = \frac{144 \, \text{m}^3}{8 \, \text{m}^3} \]
Now, perform the division:
\[ \text{Number of cubes} = 18 \]

### Final Answer
The number of cubes formed is \( 18 \).

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