The inner and outer circumferences of a circular ring are 88 cm and 110 cm respectively. Find the width of the ring.

Steps to Solve

1. Define variables

Let $C_1$ be the inner circumference, $C_2$ be the outer circumference, $r_1$ be the inner radius, and $r_2$ be the outer radius. We are given $C_1 = 44 \text{ cm}$ and $C_2 = 88 \text{ cm}$. We want to find the width of the ring, which is $r_2 - r_1$.

2. Find the inner radius $r_1$

The formula for the circumference of a circle is $C = 2 \pi r$. The inner radius is therefore

$r_1 = \frac{C_1}{2 \pi} = \frac{44}{2 \pi} = \frac{22}{\pi}$

3. Find the outer radius $r_2$

Similarly, the outer radius is

$r_2 = \frac{C_2}{2 \pi} = \frac{88}{2 \pi} = \frac{44}{\pi}$

4. Calculate the width of the ring

The width of the ring is the difference between the outer and inner radii:

$r_2 - r_1 = \frac{44}{\pi} - \frac{22}{\pi} = \frac{44 - 22}{\pi} = \frac{22}{\pi}$

5. Approximate the value

Using the approximation $\pi \approx \frac{22}{7}$, we have

$\frac{22}{\pi} \approx \frac{22}{\frac{22}{7}} = 22 \cdot \frac{7}{22} = 7$

Therefore, the width of the ring is approximately $7 \text{ cm}$.