Question

The dimensions of a metallic solid cuboid are \( 9 \, \text{m} \times 8 \, \text{m} \times 2 \, \text{m} \). It is melted and recast into cubes of dimension 2 m. Thus the number of cubes so formed will be:

• A. 18
• B. 12
• C. 16
• D. 24

Hint:

To find the number of smaller cubes that can be made from a larger solid, divide the volume of the larger solid by the volume of one smaller cube.

Answer 1

The Correct Option is C

The volume of the cuboid is calculated by multiplying its length, breadth, and height: \[ \text{Volume of cuboid} = 9 \times 8 \times 2 = 144 \, \text{m}^3 \] Next, we calculate the volume of each cube with a side length of 2 m: \[ \text{Volume of one cube} = 2^3 = 8 \, \text{m}^3 \]
Step 1: Find the number of cubes.
The number of cubes formed is the total volume of the cuboid divided by the volume of one cube: \[ \text{Number of cubes} = \frac{\text{Volume of cuboid}}{\text{Volume of one cube}} = \frac{144}{8} = 18 \]
Step 2: Conclusion.
Therefore, the number of cubes formed is 18.