How many cubes each of surface area 24 sq. dm can be made out of a metre cube, without any wastage :

Options

A. 75
B. 250
C. 125
D. 62

Answer

To solve the problem of how many cubes, each with a surface area of 24 sq. dm, can be made from a cubic meter without any wastage, we can follow these steps:

### Step 1: Understand the surface area of the cube
The surface area \( A \) of a cube is given by the formula:
\[ A = 6 \times \text{side}^2 \]
Given that the surface area is 24 sq. dm, we can set up the equation:
\[ 6 \times \text{side}^2 = 24 \]

### Step 2: Solve for the side length
To find the side length, we can rearrange the equation:
\[ \text{side}^2 = \frac{24}{6} = 4 \]
Taking the square root of both sides gives:
\[ \text{side} = \sqrt{4} = 2 \text{ dm} \]

### Step 3: Convert the side length to meters
Since we need the side length in meters, we convert decimeters to meters:
\[ 1 \text{ dm} = 0.1 \text{ m} \]
Thus,
\[ \text{side} = 2 \text{ dm} = 2 \times 0.1 \text{ m} = 0.2 \text{ m} \]

### Step 4: Calculate the volume of the cube
The volume \( V \) of a cube is given by:
\[ V = \text{side}^3 \]
Substituting the side length:
\[ V = (0.2 \text{ m})^3 = 0.2 \times 0.2 \times 0.2 = 0.008 \text{ m}^3 \]

### Step 5: Calculate the volume of the cubic meter
The volume of the original cube (1 m³) is:
\[ 1 \text{ m}^3 = 1 \text{ m}^3 \]

### Step 6: Determine how many smaller cubes can fit into the larger cube
To find the number of smaller cubes that can be made from the larger cube, we divide the volume of the larger cube by the volume of one smaller cube:
\[ \text{Number of cubes} = \frac{\text{Volume of larger cube}}{\text{Volume of smaller cube}} = \frac{1 \text{ m}^3}{0.008 \text{ m}^3} \]
Calculating this gives:
\[ \text{Number of cubes} = \frac{1}{0.008} = 125 \]

### Conclusion
Therefore, the number of cubes that can be made from a cubic meter without any wastage is **125**.

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