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 solve the problem of finding the number of cubes formed from a solid metallic cuboid, we can follow these steps:

### Step 1: Calculate the Volume of the Cuboid
The volume \( V \) of a cuboid is calculated using the formula:
\[ V = \text{length} \times \text{width} \times \text{height} \]
Given dimensions of the cuboid are \( 9 \, \text{m} \times 8 \, \text{m} \times 2 \, \text{m} \):
\[ V = 9 \times 8 \times 2 \]
\[ V = 144 \, \text{m}^3 \]

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

### Step 3: Determine the Number of Cubes Formed
Let \( x \) be the number of cubes formed. The total volume of the cubes formed must equal the volume of the cuboid:
\[ x \times \text{Volume of one cube} = \text{Volume of cuboid} \]
Substituting the volumes we calculated:
\[ x \times 8 = 144 \]
To find \( x \), divide both sides by 8:
\[ x = \frac{144}{8} \]
\[ x = 18 \]

### Conclusion
The number of cubes formed from the cuboid is \( 18 \).

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