We are given a circle with center O and diameter AC. The measure of angle $COB$ is $48^\circ$, and the radius of the circle is 8 cm. We need to find the length of arc $BC$.

1. Problem Description

We are given a circle with center O and diameter AC. The measure of angle $COB$ is $48^\circ$, and the radius of the circle is 8 cm. We need to find the length of arc $BC$.

2. Solution Steps

The formula for the arc length is:

$$\text{Arc length} = \frac{\text{central angle}}{360^\circ} \times 2\pi r$$

where $r$ is the radius of the circle.

In this case, the central angle is $\angle COB = 48^\circ$ and the radius $r = 8$ cm.

Plugging these values into the formula:

$$\text{Arc length } BC = \frac{48^\circ}{360^\circ} \times 2\pi (8)$$

$$\text{Arc length } BC = \frac{48}{360} \times 16\pi$$

$$\text{Arc length } BC = \frac{2}{15} \times 16\pi = \frac{32\pi}{15}$$

Now, we approximate the value:

$$\text{Arc length } BC \approx \frac{32 \times 3.14159}{15} = \frac{100.53088}{15} \approx 6.702$$

Rounding to the nearest tenth of a cm, we get 6.7 cm.

3. Final Answer

6.7 cm