If the circumferences of two concentric circles forming a ring are 88 cm and 66 cm respectively, then the width of the ring is :

Options

A. 14 cm
B. 10.5 cm
C. 3.5 cm
D. 22 cm

Answer

To find the width of the ring formed by two concentric circles with given circumferences, we will follow these steps:

### Step 1: Understand the Problem
We have two concentric circles with circumferences of 88 cm and 66 cm. The width of the ring is the difference between the radii of the two circles.

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

### Step 3: Calculate the Radii of the Circles
1. For the outer circle (circumference = 88 cm):
\[ r_1 = \frac{C_1}{2\pi} = \frac{88}{2\pi} = \frac{44}{\pi} \text{ cm} \]

2. For the inner circle (circumference = 66 cm):
\[ r_2 = \frac{C_2}{2\pi} = \frac{66}{2\pi} = \frac{33}{\pi} \text{ cm} \]

### Step 4: Calculate the Width of the Ring
The width of the ring is the difference between the radii of the two circles:
\[ \text{Width} = r_1 - r_2 = \frac{44}{\pi} - \frac{33}{\pi} = \frac{44 - 33}{\pi} = \frac{11}{\pi} \text{ cm} \]

### Step 5: Approximate the Width
Using \( \pi \approx 3.14 \):
\[ \text{Width} \approx \frac{11}{3.14} \approx 3.5 \text{ cm} \]

### Final Answer
The width of the ring is approximately **3.5 cm**.

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