How many square sheets of coloured paper of side 30 cm would be required to cover a wooden box having length, breadth and height as 90 cm, 60 cm and 30 cm respectively ?

Options

A. `22`
B. `23`
C. `24`
D. `25`

Explanation

To solve the problem of how many square sheets of colored paper of side 30 cm are required to cover a wooden box with dimensions 90 cm (length), 60 cm (breadth), and 30 cm (height), we will follow these steps:

### Step 1: Calculate the Total Surface Area of the Box
The formula for the total surface area (TSA) of a rectangular box is given by:
\[ \text{TSA} = 2 \times (l \times b + b \times h + h \times l) \]
Where:
- \( l \) = length of the box = 90 cm
- \( b \) = breadth of the box = 60 cm
- \( h \) = height of the box = 30 cm

Substituting the values:
\[ \text{TSA} = 2 \times (90 \times 60 + 60 \times 30 + 30 \times 90) \]

Calculating each term:
- \( 90 \times 60 = 5400 \)
- \( 60 \times 30 = 1800 \)
- \( 30 \times 90 = 2700 \)

Now, summing these:
\[ 5400 + 1800 + 2700 = 9900 \]

Now, multiply by 2:
\[ \text{TSA} = 2 \times 9900 = 19800 \, \text{cm}^2 \]

### Step 2: Calculate the Area of Each Sheet of Paper
The area of one square sheet of colored paper with side 30 cm is calculated as:
\[ \text{Area of one sheet} = \text{side}^2 = 30 \times 30 = 900 \, \text{cm}^2 \]

### Step 3: Calculate the Number of Sheets Required
To find the number of sheets required, we divide the total surface area of the box by the area of one sheet of paper:
\[ n = \frac{\text{TSA of the box}}{\text{Area of one sheet}} = \frac{19800}{900} \]

Calculating this gives:
\[ n = 22 \]

### Conclusion
Thus, the number of square sheets of colored paper required to cover the wooden box is **22**.

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