The dimensions of a cuboid are `8mxx6mxx4m`.Its lateral surface area is

Options

A. `210 m^(2)`
B. `105 m^(2)`
C. `112 m^(2)`
D. `240 m^(2)`

Answer

To find the lateral surface area of the cuboid with dimensions 8 m, 6 m, and 4 m, we can follow these steps:

### Step 1: Identify the dimensions
The dimensions of the cuboid are:
- Length (L) = 8 m
- Breadth (B) = 6 m
- Height (H) = 4 m

### Step 2: Understand the formula for lateral surface area
The formula for the lateral surface area (LSA) of a cuboid is given by:
\[ \text{LSA} = 2 \times (L + B) \times H \]
This formula accounts for the areas of the four vertical sides of the cuboid.

### Step 3: Substitute the values into the formula
Now, we will substitute the values of L, B, and H into the formula:
\[ \text{LSA} = 2 \times (8 + 6) \times 4 \]

### Step 4: Calculate the sum of Length and Breadth
First, calculate the sum of Length and Breadth:
\[ 8 + 6 = 14 \]

### Step 5: Multiply the sum by Height
Next, multiply the result by the Height:
\[ 14 \times 4 = 56 \]

### Step 6: Multiply by 2
Finally, multiply the result by 2 to get the lateral surface area:
\[ \text{LSA} = 2 \times 56 = 112 \, \text{m}^2 \]

### Conclusion
The lateral surface area of the cuboid is \( 112 \, \text{m}^2 \).

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