Find the volume the total surface area and the lateral surface area of a cuboid which is 8 m long, 6 m broad and 3.5 m high.

Answer

To find the volume, total surface area, and lateral surface area of a cuboid with given dimensions, we can follow these steps:

### Step 1: Identify the dimensions of the cuboid
- Length (l) = 8 m
- Breadth (b) = 6 m
- Height (h) = 3.5 m

### Step 2: Calculate the volume of the cuboid
The formula for the volume \( V \) of a cuboid is:
\[ V = l \times b \times h \]
Substituting the values:
\[ V = 8 \, \text{m} \times 6 \, \text{m} \times 3.5 \, \text{m} \]
Calculating step-by-step:
1. First, calculate \( 8 \times 6 = 48 \).
2. Next, calculate \( 48 \times 3.5 = 168 \).

Thus, the volume of the cuboid is:
\[ V = 168 \, \text{m}^3 \]

### Step 3: Calculate the total surface area of the cuboid
The formula for the total surface area \( A \) of a cuboid is:
\[ A = 2(l \times b + b \times h + h \times l) \]
Substituting the values:
\[ A = 2(8 \times 6 + 6 \times 3.5 + 3.5 \times 8) \]
Calculating step-by-step:
1. Calculate \( 8 \times 6 = 48 \).
2. Calculate \( 6 \times 3.5 = 21 \).
3. Calculate \( 3.5 \times 8 = 28 \).
4. Now sum these results: \( 48 + 21 + 28 = 97 \).
5. Finally, multiply by 2: \( 2 \times 97 = 194 \).

Thus, the total surface area of the cuboid is:
\[ A = 194 \, \text{m}^2 \]

### Step 4: Calculate the lateral surface area of the cuboid
The formula for the lateral surface area \( L \) of a cuboid is:
\[ L = 2(h \times (l + b)) \]
Substituting the values:
\[ L = 2(3.5 \times (8 + 6)) \]
Calculating step-by-step:
1. First, calculate \( 8 + 6 = 14 \).
2. Then calculate \( 3.5 \times 14 = 49 \).
3. Finally, multiply by 2: \( 2 \times 49 = 98 \).

Thus, the lateral surface area of the cuboid is:
\[ L = 98 \, \text{m}^2 \]

### Final Results
- Volume of the cuboid: \( 168 \, \text{m}^3 \)
- Total surface area of the cuboid: \( 194 \, \text{m}^2 \)
- Lateral surface area of the cuboid: \( 98 \, \text{m}^2 \)

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