How many envelopes can be made out of a sheet of paper 72 cm by 48 cm, if each envelope requires a paper of size 18 cm by 12 cm?

Options

A. 4
B. 8
C. 12
D. 16

Answer

To solve the problem of how many envelopes can be made from a sheet of paper measuring 72 cm by 48 cm, with each envelope requiring a paper size of 18 cm by 12 cm, we will follow these steps:

### Step 1: Calculate the area of the sheet of paper.
The area of a rectangle is given by the formula:
\[ \text{Area} = \text{Length} \times \text{Breadth} \]

For the sheet of paper:
- Length = 72 cm
- Breadth = 48 cm

So, the area of the sheet is:
\[ \text{Area of sheet} = 72 \, \text{cm} \times 48 \, \text{cm} = 3456 \, \text{cm}^2 \]

### Step 2: Calculate the area of one envelope.
Using the same formula for the area of a rectangle, we calculate the area of one envelope:
- Length = 18 cm
- Breadth = 12 cm

So, the area of one envelope is:
\[ \text{Area of envelope} = 18 \, \text{cm} \times 12 \, \text{cm} = 216 \, \text{cm}^2 \]

### Step 3: Determine how many envelopes can be made.
To find out how many envelopes can be made from the sheet of paper, we divide the area of the sheet by the area of one envelope:
\[ \text{Number of envelopes} = \frac{\text{Area of sheet}}{\text{Area of envelope}} \]

Substituting the areas we calculated:
\[ \text{Number of envelopes} = \frac{3456 \, \text{cm}^2}{216 \, \text{cm}^2} = 16 \]

### Conclusion:
Therefore, the number of envelopes that can be made from the sheet of paper is **16**.

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