From a circle, a sector with a central angle of 30° is cut off. If the length of the arc of this sector is 5.5 cm, then find the radius (in cm) of the circle. (Use $\pi =\frac{22}{7}$)

Given Data:

Central angle of the sector ($\theta$) = 30°
Length of the arc ($l$) = 5.5 cm
Value of $\pi =\frac{22}{7}$

The correct option is 10.5.

Formula:

The length of an arc of a sector with central angle $\theta$ and radius $r$ is given by:

$l=\frac{\theta }{360°}\times 2\pi r$

Step-by-Step Calculation:

Substitute the given values into the formula:

$5.5=\frac{30°}{360°}\times 2\times \frac{22}{7}\times r$

Simplify the fraction $\frac{30°}{360°}$:

$5.5=\frac{1}{12}\times 2\times \frac{22}{7}\times r$

Simplify $\frac{2}{12}$ to $\frac{1}{6}$:

$5.5=\frac{1}{6}\times \frac{22}{7}\times r$

$5.5=\frac{22}{42}\times r$

Now, solve for the radius ($r$):

$r=\frac{5.5\times 42}{22}$

Divide 22 by 5.5, which gives 4:

$r=\frac{42}{4}$

$r=10.5\text{cm}$

Thus, the radius of the circle is 10.5 cm.