How many circular discs, each of 4 cm radius , can be cut from the rectangular metal sheet with dimensions :
75 cm and 48 cm

Answer

To solve the problem of how many circular discs, each with a radius of 4 cm, can be cut from a rectangular metal sheet with dimensions 75 cm by 48 cm, we will follow these steps:

### Step 1: Calculate the area of the rectangular metal sheet.
The area \( A \) of a rectangle is given by the formula:
\[ A = \text{length} \times \text{breadth} \]
Here, the length is 75 cm and the breadth is 48 cm.

\[ A = 75 \, \text{cm} \times 48 \, \text{cm} = 3600 \, \text{cm}^2 \]

### Step 2: Calculate the area of one circular disc.
The area \( A \) of a circle is given by the formula:
\[ A = \pi r^2 \]
where \( r \) is the radius of the circle. Given that the radius is 4 cm, we can substitute this value into the formula.

\[ A = \pi \times (4 \, \text{cm})^2 = \pi \times 16 \, \text{cm}^2 \]
Using \( \pi \approx 3.14 \):
\[ A \approx 3.14 \times 16 \, \text{cm}^2 = 50.24 \, \text{cm}^2 \]

### Step 3: Calculate the number of circular discs that can be cut from the rectangular sheet.
To find the number of discs that can be cut, we divide the area of the rectangle by the area of one disc.

\[ \text{Number of discs} = \frac{\text{Area of rectangle}}{\text{Area of one disc}} = \frac{3600 \, \text{cm}^2}{50.24 \, \text{cm}^2} \]

Calculating this gives:
\[ \text{Number of discs} \approx 71.6 \]

Since we cannot cut a fraction of a disc, we take the whole number, which is 71.

### Final Answer:
Thus, the number of circular discs that can be cut from the rectangular metal sheet is **71**.

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