A sheet is 11 cm long and 2 cm wide. Circular piece of diameter 0.5 cm are cut from it. Calculate the number of discs that can be prepared.

Answer

To solve the problem of how many circular discs can be cut from a rectangular sheet, we will follow these steps:

### Step 1: Calculate the Area of the Rectangular Sheet
The area \( A \) of a rectangle is given by the formula:
\[ A = \text{length} \times \text{width} \]
Here, the length of the sheet is 11 cm and the width is 2 cm.

\[ A = 11 \, \text{cm} \times 2 \, \text{cm} = 22 \, \text{cm}^2 \]

### Step 2: Calculate the Area of One Circular Disc
The area \( A_d \) of a circle is given by the formula:
\[ A_d = \pi r^2 \]
where \( r \) is the radius of the circle. The diameter of the circular piece is given as 0.5 cm, so the radius \( r \) is:
\[ r = \frac{\text{diameter}}{2} = \frac{0.5 \, \text{cm}}{2} = 0.25 \, \text{cm} \]
Now, substituting the radius into the area formula:
\[ A_d = \pi (0.25 \, \text{cm})^2 = \pi \times 0.0625 \, \text{cm}^2 \]
Using \( \pi \approx \frac{22}{7} \):
\[ A_d = \frac{22}{7} \times 0.0625 \approx 0.196 \, \text{cm}^2 \]

### Step 3: Calculate the Number of Discs
To find the number of discs that can be cut from the sheet, divide the area of the sheet by the area of one disc:
\[ \text{Number of discs} = \frac{\text{Area of the sheet}}{\text{Area of one disc}} = \frac{22 \, \text{cm}^2}{0.196 \, \text{cm}^2} \]
Calculating this gives:
\[ \text{Number of discs} \approx 112 \]

### Final Answer
Thus, the number of circular discs that can be prepared from the sheet is **112**.

---