Find the length of the arc whose central angle is $90^{\circ }$ and the radius of the circle is $3.5\text{cm}$.

The formula for the length of an arc is:
$$\text{Length of arc}=\frac{\theta }{360^{\circ }}\times 2\pi r$$
Given:Central angle ($\theta$) = $90^{\circ }$ Radius ($r$) = $3.5\text{cm}=\frac{7}{2}\text{cm}$ Take $\pi \approx \frac{22}{7}$ Substitute the values into the formula:
$$\text{Length of arc}=\frac{90^{\circ }}{360^{\circ }}\times 2\times \frac{22}{7}\times \frac{7}{2}$$
$$\text{Length of arc}=\frac{1}{4}\times 22=5.5\text{cm}$$
Therefore, the length of the arc is $5.5\text{cm}$.