A rectangular sheet of cardboard has a length of 4 cm and a breadth of 2 cm. The largest possible circle is cut from this sheet. Find the area of the remaining portion of the sheet.

Points to Remember:

• Area of a rectangle = length × breadth
• Area of a circle = πr² (where r is the radius)
• The largest possible circle that can be cut from a rectangle has a diameter equal to the smaller dimension of the rectangle.

Introduction:

This question involves calculating the area of a rectangle and a circle to determine the area of the remaining portion of the rectangle after a circle is cut out. The problem tests understanding of basic geometric shapes and area calculations. We are given a rectangular sheet of cardboard with dimensions 4 cm (length) and 2 cm (breadth). The largest circle that can be cut from this sheet will have a diameter of 2 cm (the smaller dimension). We need to find the area of the cardboard remaining after this circle is removed.

Body:

1. Area of the Rectangular Sheet:

The area of the rectangular sheet is calculated as follows:

Area of rectangle = length × breadth = 4 cm × 2 cm = 8 cm²

2. Area of the Largest Possible Circle:

The diameter of the largest possible circle that can be cut from the sheet is equal to the smaller dimension of the rectangle, which is 2 cm. Therefore, the radius (r) of the circle is 2 cm / 2 = 1 cm.

The area of the circle is calculated using the formula:

Area of circle = πr² = π × (1 cm)² = π cm² ≈ 3.14 cm² (using π ≈ 3.14)

3. Area of the Remaining Portion:

The area of the remaining portion of the sheet is the difference between the area of the rectangle and the area of the circle:

Area of remaining portion = Area of rectangle – Area of circle = 8 cm² – π cm² ≈ 8 cm² – 3.14 cm² ≈ 4.86 cm²

Conclusion:

In summary, the area of the rectangular sheet is 8 cm², and the area of the largest possible circle that can be cut from it is approximately 3.14 cm². Therefore, the area of the remaining portion of the sheet after the circle is cut out is approximately 4.86 cm². This problem highlights the practical application of geometric formulas in solving real-world problems involving shapes and areas. Understanding these basic concepts is crucial for further studies in geometry and related fields. No specific policy recommendations or best practices are applicable to this purely mathematical problem. The solution demonstrates a clear and concise approach to solving geometric problems, emphasizing accuracy and precision in calculations.