The dimensions of a solid metallic cuboid are 36cm, 54cm and 24cm. It is melted and recast into 8 cubes of same volume. The sum of the surface areas (in `cm^(2)`) of these 8 cubes is:

Options

A. 10368
B. 11664
C. 9720
D. 15552

Answer

To solve the problem step by step, 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 dimensions are:
- Length = 36 cm
- Breadth = 54 cm
- Height = 24 cm

Now substituting the values:
\[ V = 36 \times 54 \times 24 \]

### Step 2: Calculate the Volume
Now, we will perform the multiplication:
\[ V = 36 \times 54 = 1944 \]
Next, multiply this result by 24:
\[ V = 1944 \times 24 = 46656 \text{ cm}^3 \]

### Step 3: Find the Volume of One Cube
Since the cuboid is melted and recast into 8 cubes of the same volume, the volume of one cube \( V_{\text{cube}} \) is:
\[ V_{\text{cube}} = \frac{V}{8} = \frac{46656}{8} = 5820.75 \text{ cm}^3 \]

### Step 4: Calculate the Side Length of One Cube
The volume of a cube is given by:
\[ V_{\text{cube}} = \text{side}^3 \]
To find the side length, we take the cube root:
\[ \text{side} = \sqrt[3]{5820.75} \]
Calculating the cube root:
\[ \text{side} \approx 18 \text{ cm} \]

### Step 5: Calculate the Surface Area of One Cube
The surface area \( SA \) of a cube is given by:
\[ SA = 6 \times \text{side}^2 \]
Substituting the side length:
\[ SA = 6 \times 18^2 = 6 \times 324 = 1944 \text{ cm}^2 \]

### Step 6: Calculate the Total Surface Area of 8 Cubes
Since there are 8 cubes, the total surface area \( SA_{\text{total}} \) is:
\[ SA_{\text{total}} = 8 \times SA = 8 \times 1944 = 15552 \text{ cm}^2 \]

### Final Answer
The sum of the surface areas of the 8 cubes is:
\[ \boxed{15552 \text{ cm}^2} \]