If the radii of two circles is 6.5 cm and 9.3 cm then find the difference between the circumference of the circles.

Options

A. 17.6 cm
B. 16.8 cm
C. 19.2 cm
D. 15.6 cm

Answer

To find the difference between the circumferences of two circles with radii of 6.5 cm and 9.3 cm, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the formula for circumference**:
The formula for the circumference \( C \) of a circle is given by:
\[ C = 2 \pi r \]
where \( r \) is the radius of the circle.

2. **Calculate the circumference of the first circle (radius = 9.3 cm)**:
\[ C_1 = 2 \pi (9.3) \]
Using \( \pi \approx \frac{22}{7} \):
\[ C_1 = 2 \times \frac{22}{7} \times 9.3 \]

3. **Calculate the circumference of the second circle (radius = 6.5 cm)**:
\[ C_2 = 2 \pi (6.5) \]
Again using \( \pi \approx \frac{22}{7} \):
\[ C_2 = 2 \times \frac{22}{7} \times 6.5 \]

4. **Find the difference between the two circumferences**:
\[ \text{Difference} = C_1 - C_2 \]

5. **Perform the calculations**:
- For \( C_1 \):
\[ C_1 = 2 \times \frac{22}{7} \times 9.3 = \frac{44 \times 9.3}{7} = \frac{409.2}{7} \approx 58.4 \text{ cm} \]
- For \( C_2 \):
\[ C_2 = 2 \times \frac{22}{7} \times 6.5 = \frac{44 \times 6.5}{7} = \frac{286}{7} \approx 40.857 \text{ cm} \]
- Now calculate the difference:
\[ \text{Difference} = 58.4 - 40.857 \approx 17.543 \text{ cm} \]

6. **Round the answer**:
The difference in circumference can be rounded to one decimal place:
\[ \text{Difference} \approx 17.6 \text{ cm} \]

### Final Answer:
The difference between the circumferences of the circles is approximately **17.6 cm**.