To find the length of the arc $ABC$ in the circle, use the following approach:

Given Information:

• The radius $r = 32 \, \text{cm}$.
• The central angle $\theta = 90^\circ$.
• Use $\pi \approx 3.14$.

Step-by-Step Solution:

1. The formula for the length of an arc is: $\text{Arc Length} = \frac{\theta}{360^\circ} \times 2\pi r$
2. Substitute the values into the formula: $\text{Arc Length} = \frac{90^\circ}{360^\circ} \times 2 \times 3.14 \times 32$
3. Simplify the fraction: $\frac{90}{360} = \frac{1}{4}$
4. Now calculate the arc length: $\text{Arc Length} = \frac{1}{4} \times 2 \times 3.14 \times 32$
5. Compute step-by-step: $2 \times 3.14 = 6.28,$ $6.28 \times 32 = 200.96,$ $\frac{1}{4} \times 200.96 = 50.24 \, \text{cm}.$

Final Answer:

The length of arc $ABC$ is 50.24 cm.

Would you like more details or have any questions?

Here are 5 related questions you can try:

1. What is the formula for the circumference of a circle?
2. How do you calculate the area of a sector given a central angle?
3. If the angle was $180^\circ$, what would the arc length be?
4. How does the arc length change if the radius is doubled?
5. How do you find the central angle if the arc length and radius are known?

Tip: Always express angles in degrees or radians consistently when using arc length formulas.