If l,b,h be the length, breadth and height of a cuboid, then its whole surface area =(……….) sq units.

Answer

To find the whole surface area of a cuboid with length \( l \), breadth \( b \), and height \( h \), we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Structure of the Cuboid**:
A cuboid has six faces, and each face is a rectangle. The dimensions of the cuboid are given as length \( l \), breadth \( b \), and height \( h \).

**Hint**: Remember that a cuboid has opposite faces that are equal in area.

2. **Calculate the Area of Each Pair of Faces**:
- The area of the bottom face (length \( l \) and breadth \( b \)) is calculated as:
\[ \text{Area}_{\text{bottom}} = l \times b \]
- The area of the top face is the same as the bottom face:
\[ \text{Area}_{\text{top}} = l \times b \]
- The area of the front face (length \( l \) and height \( h \)) is:
\[ \text{Area}_{\text{front}} = l \times h \]
- The area of the back face is the same as the front face:
\[ \text{Area}_{\text{back}} = l \times h \]
- The area of the left face (breadth \( b \) and height \( h \)) is:
\[ \text{Area}_{\text{left}} = b \times h \]
- The area of the right face is the same as the left face:
\[ \text{Area}_{\text{right}} = b \times h \]

3. **Sum the Areas of All Faces**:
Now, we can sum the areas of all six faces:
\[ \text{Total Surface Area} = \text{Area}_{\text{bottom}} + \text{Area}_{\text{top}} + \text{Area}_{\text{front}} + \text{Area}_{\text{back}} + \text{Area}_{\text{left}} + \text{Area}_{\text{right}} \]
Substituting the areas calculated:
\[ \text{Total Surface Area} = (l \times b) + (l \times b) + (l \times h) + (l \times h) + (b \times h) + (b \times h) \]

4. **Combine Like Terms**:
Combine the like terms:
\[ \text{Total Surface Area} = 2(l \times b) + 2(l \times h) + 2(b \times h) \]

5. **Factor Out the Common Factor**:
We can factor out the common factor of 2:
\[ \text{Total Surface Area} = 2(lb + lh + bh) \]

### Final Answer:
Thus, the whole surface area of the cuboid is given by:
\[ \text{Whole Surface Area} = 2(lb + lh + bh) \text{ sq units} \]