A cuboid of size 50 cm × 40 cm × 30 cm is cut into 8 identical parts by 3 cuts. What is the total surface area (in `cm^2` ) of all the 8 parts?

Options

A. 11750
B. 14100
C. 18800
D. 23500

Answer

To solve the problem of finding the total surface area of the 8 identical parts obtained from cutting a cuboid of dimensions 50 cm × 40 cm × 30 cm, we can follow these steps:

### Step 1: Understand the dimensions of the original cuboid
The original dimensions of the cuboid are:
- Length (L) = 50 cm
- Width (W) = 40 cm
- Height (H) = 30 cm

### Step 2: Determine how the cuboid is cut
The cuboid is cut into 8 identical parts using 3 cuts. To achieve 8 parts, we can make the following cuts:
- Cut along the length (50 cm) into 2 parts: Each part will be 25 cm long.
- Cut along the width (40 cm) into 2 parts: Each part will be 20 cm wide.
- Cut along the height (30 cm) into 2 parts: Each part will be 15 cm high.

So, the dimensions of each of the 8 identical parts (new cuboids) will be:
- Length = 25 cm
- Width = 20 cm
- Height = 15 cm

### Step 3: Calculate the surface area of one part
The formula for the total surface area (TSA) of a cuboid is given by:
\[ \text{TSA} = 2(LW + LH + WH) \]
Substituting the dimensions of one part:
- L = 25 cm
- W = 20 cm
- H = 15 cm

Calculating each term:
1. \( LW = 25 \times 20 = 500 \)
2. \( LH = 25 \times 15 = 375 \)
3. \( WH = 20 \times 15 = 300 \)

Now, substituting these values into the TSA formula:
\[ \text{TSA} = 2(500 + 375 + 300) = 2(1175) = 2350 \text{ cm}^2 \]

### Step 4: Calculate the total surface area of all 8 parts
Since there are 8 identical parts:
\[ \text{Total Surface Area of 8 parts} = 8 \times \text{TSA of one part} = 8 \times 2350 = 18800 \text{ cm}^2 \]

### Final Answer
The total surface area of all 8 parts is **18800 cm²**.

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