What is the radius of the largest circle that can be cut out of the rectangle measuring 10 cm in length and 8 cm in breadth?

Options

A. 4 cm
B. 5 cm
C. 8 cm
D. 10 cm

Answer

To find the radius of the largest circle that can be cut out of a rectangle measuring 10 cm in length and 8 cm in breadth, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the dimensions of the rectangle**:
- Length = 10 cm
- Breadth = 8 cm

2. **Understand the constraints for the circle**:
- The largest circle that can fit inside the rectangle must have its diameter equal to the smaller dimension of the rectangle. This is because the circle must fit entirely within the rectangle.

3. **Determine the diameter of the largest circle**:
- The smaller dimension of the rectangle is the breadth, which is 8 cm. Therefore, the diameter of the largest circle that can fit inside the rectangle is 8 cm.

4. **Calculate the radius of the circle**:
- The radius (r) of a circle is half of its diameter (d).
- So, \( r = \frac{d}{2} = \frac{8 \text{ cm}}{2} = 4 \text{ cm} \).

5. **Conclusion**:
- The radius of the largest circle that can be cut out of the rectangle is 4 cm.

### Final Answer:
The radius of the largest circle that can be cut out of the rectangle is **4 cm**.