Find the total surface area (in `cm^2`) of a cuboid of length, breadth and height of 10.5 cm, 8cm and 9cm respectively.

Options

A. 607
B. 767
C. 769
D. 501

Answer

To find the total surface area of a cuboid, we can use the formula:

\[ \text{Total Surface Area} = 2(lb + bh + hl) \]

where:
- \( l \) = length
- \( b \) = breadth
- \( h \) = height

Given:
- Length \( l = 10.5 \, \text{cm} \)
- Breadth \( b = 8 \, \text{cm} \)
- Height \( h = 9 \, \text{cm} \)

### Step 1: Calculate the area of each pair of opposite faces
1. Calculate \( lb \):
\[ lb = 10.5 \times 8 = 84 \, \text{cm}^2 \]

2. Calculate \( bh \):
\[ bh = 8 \times 9 = 72 \, \text{cm}^2 \]

3. Calculate \( hl \):
\[ hl = 9 \times 10.5 = 94.5 \, \text{cm}^2 \]

### Step 2: Sum the areas of the pairs of opposite faces
Now, we will sum these areas:
\[ lb + bh + hl = 84 + 72 + 94.5 = 250.5 \, \text{cm}^2 \]

### Step 3: Multiply by 2 to find the total surface area
Finally, we multiply the sum by 2 to get the total surface area:
\[ \text{Total Surface Area} = 2 \times 250.5 = 501 \, \text{cm}^2 \]

### Conclusion
Thus, the total surface area of the cuboid is:
\[ \boxed{501 \, \text{cm}^2} \]