Two equal maximum sized circular plates are cut off from a circular paper sheet of circumference 352 cm. Then the circumference of each circular plat is

Options

A. 176 cm
B. 150 cm
C. 165 cm
D. 180 cm

Answer

To solve the problem, we need to find the circumference of each of the two equal maximum sized circular plates that are cut from a circular paper sheet with a given circumference of 352 cm.

### Step-by-Step Solution:

1. **Understand the Given Information**:
- The circumference of the circular paper sheet is given as 352 cm.

2. **Use the Formula for Circumference**:
- The formula for the circumference \( C \) of a circle is:
\[ C = 2 \pi r \]
- Here, \( r \) is the radius of the circle.

3. **Calculate the Radius of the Original Circle**:
- Rearranging the formula to find the radius:
\[ r = \frac{C}{2 \pi} \]
- Substituting the given circumference:
\[ r = \frac{352 \text{ cm}}{2 \times \frac{22}{7}} = \frac{352 \text{ cm}}{\frac{44}{7}} = 352 \times \frac{7}{44} \]
- Simplifying this:
\[ r = 352 \div 44 \times 7 = 8 \times 7 = 56 \text{ cm} \]

4. **Determine the Diameter of the Original Circle**:
- The diameter \( d \) of the circle is given by:
\[ d = 2r = 2 \times 56 \text{ cm} = 112 \text{ cm} \]

5. **Calculate the Diameter of Each Circular Plate**:
- Since two equal maximum sized circular plates are cut from the original circle, the diameter of each plate \( d_{plate} \) is:
\[ d_{plate} = \frac{d}{2} = \frac{112 \text{ cm}}{2} = 56 \text{ cm} \]

6. **Calculate the Circumference of Each Circular Plate**:
- Now, we can calculate the circumference of each plate using the diameter:
\[ C_{plate} = \pi d_{plate} = \frac{22}{7} \times 56 \text{ cm} \]
- Simplifying this:
\[ C_{plate} = \frac{22 \times 56}{7} = \frac{1232}{7} \text{ cm} = 176 \text{ cm} \]

### Final Answer:
The circumference of each circular plate is **176 cm**.