To solve the problem, we need to find the length of the arc $\text{ABC}$. Here's the step-by-step process:

Step 1: Arc Length Formula

The formula to find the arc length $L$ is:

$L = 2\pi r \cdot \frac{\theta}{360^\circ}$

Where:

• $r$ is the radius of the circle.
• $\theta$ is the central angle in degrees.

Step 2: Substitute the Given Values

From the diagram:

• Radius $r = 52 \, \text{cm}$
• Central angle $\theta = 270^\circ$
• Use $\pi \approx 3.14$

Substitute these into the formula:

$L = 2 \cdot 3.14 \cdot 52 \cdot \frac{270}{360}$

Step 3: Simplify the Expression

1. Simplify the fraction $\frac{270}{360}$:

$\frac{270}{360} = 0.75$

2. Multiply the constants:

$L = 2 \cdot 3.14 \cdot 52 \cdot 0.75$

$L = 3.14 \cdot 104 \cdot 0.75$

$L = 244.92 \, \text{cm}$

Final Answer

The length of the arc $\text{ABC}$ is:

$\boxed{244.92 \, \text{cm}}$

This result is rounded to the nearest hundredth as requested.

Would you like further clarification or a breakdown of specific steps? Let me know!

Related Questions to Expand Knowledge

1. How is the arc length formula derived from the circumference formula?
2. What is the length of a full semicircular arc with the same radius?
3. How would the arc length change if the angle were $180^\circ$ instead of $270^\circ$?
4. Can you use radians instead of degrees to calculate arc length?
5. What is the total circumference of the circle in this problem?

Tip

Always double-check your angle measurement unit (degrees vs. radians) to ensure you use the correct formula for arc length!