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 step by step, we will follow these calculations:

### Step 1: Calculate the area of the sheet.
The area of a rectangle (sheet) is given by the formula:
\[ \text{Area} = \text{Length} \times \text{Breadth} \]
Given:
- Length of the sheet = 11 cm
- Breadth of the sheet = 2 cm

Calculating the area:
\[ \text{Area of the sheet} = 11 \, \text{cm} \times 2 \, \text{cm} = 22 \, \text{cm}^2 \]

### Step 2: Calculate the radius of the circular piece.
The diameter of the circular piece is given as 0.5 cm. The radius (r) is half of the diameter:
\[ r = \frac{\text{Diameter}}{2} = \frac{0.5 \, \text{cm}}{2} = 0.25 \, \text{cm} \]

### Step 3: Calculate the area of the circular piece (disc).
The area of a circle is given by the formula:
\[ \text{Area} = \pi r^2 \]
Substituting the radius:
\[ \text{Area of the disc} = \pi \times (0.25 \, \text{cm})^2 = \pi \times 0.0625 \, \text{cm}^2 \]
Using \(\pi \approx \frac{22}{7}\):
\[ \text{Area of the disc} = \frac{22}{7} \times 0.0625 \, \text{cm}^2 \]
Calculating:
\[ \text{Area of the disc} = \frac{22 \times 0.0625}{7} = \frac{1.375}{7} \, \text{cm}^2 \]

### Step 4: Calculate the number of discs that can be cut from the sheet.
To find the number of discs, divide the area of the sheet by the area of one disc:
\[ \text{Number of discs} = \frac{\text{Area of the sheet}}{\text{Area of the disc}} = \frac{22 \, \text{cm}^2}{\frac{1.375}{7} \, \text{cm}^2} \]
This simplifies to:
\[ \text{Number of discs} = 22 \times \frac{7}{1.375} \]
Calculating:
\[ \text{Number of discs} = \frac{154}{1.375} \approx 112 \]

### Final Answer:
The number of discs that can be prepared from the sheet is **112 discs**.

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