The inner and outer circumference of a circular ring is 22 cm and 44 cm, respectively. What is the thickness of the ring?

Options

A. 2.5 cm
B. 1.5 cm
C. 5.5 cm
D. 3.5 cm

Answer

To find the thickness of the circular ring, we need to follow these steps:

### Step-by-Step Solution:

1. **Identify the given values**:
- Inner circumference (C_inner) = 22 cm
- Outer circumference (C_outer) = 44 cm

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

3. **Calculate the inner radius (r)**:
From the inner circumference:
\[ C_{\text{inner}} = 2\pi r \]
Substitute the value of C_inner:
\[ 22 = 2\pi r \]
Rearranging gives:
\[ r = \frac{22}{2\pi} = \frac{11}{\pi} \text{ cm} \]

4. **Calculate the outer radius (R)**:
From the outer circumference:
\[ C_{\text{outer}} = 2\pi R \]
Substitute the value of C_outer:
\[ 44 = 2\pi R \]
Rearranging gives:
\[ R = \frac{44}{2\pi} = \frac{22}{\pi} \text{ cm} \]

5. **Calculate the thickness of the ring**:
The thickness (T) of the ring is the difference between the outer radius and the inner radius:
\[ T = R - r \]
Substitute the values of R and r:
\[ T = \frac{22}{\pi} - \frac{11}{\pi} \]
Simplifying gives:
\[ T = \frac{22 - 11}{\pi} = \frac{11}{\pi} \text{ cm} \]

6. **Convert the thickness to a numerical value**:
Using the approximate value of \(\pi \approx \frac{22}{7}\):
\[ T = \frac{11}{\pi} = \frac{11 \times 7}{22} = \frac{77}{22} = 3.5 \text{ cm} \]

### Final Answer:
The thickness of the circular ring is **3.5 cm**.