To solve this problem, we need to calculate the arc length of the given partial circle. The formula for the arc length $L$ of a circle is:

$L = r \theta$

where:

• $r$ is the radius of the circle,
• $\theta$ is the central angle of the arc in radians.

From the image:

• The radius $r$ is given as $4$ units,
• The central angle is $90^\circ$, which we need to convert to radians: $\theta = \frac{90^\circ \times \pi}{180^\circ} = \frac{\pi}{2} \, \text{radians}.$

Substituting into the formula: $L = 4 \cdot \frac{\pi}{2} = 2\pi \, \text{units}.$

Final Answer:

The arc length is $2\pi \, \text{units}$. Alternatively, if $\pi$ is approximated as $3.14$: $L = 2 \cdot 3.14 = 6.28 \, \text{units}.$

Would you like a further explanation or related details?

Related Questions:

1. How would the arc length change if the angle were $180^\circ$ instead?
2. What is the relationship between arc length and the circumference of the circle?
3. How can you calculate the arc length if the central angle is given in radians?
4. What is the full circumference of this circle?
5. How does the radius affect the arc length for a fixed angle?

Tip:

Always convert angles to radians when using