Question

The sector of a circle shown to the left has its center at point OO. The arc XYZXYZ has length 10.810.8, and the central angle XOZXOZ has measure 1.81.8 radians. What is the radius length, rr, of the sector?]

Answer 1

Answer: Length of the radius of the sector is 6 units.

Step-by-step explanation:

Since we have given that

Length of an arc = 10.8

Radian of a central angle = 1.8

First we convert radian into degrees,

$1\ radian= 57.295779513\textdegree\\\\1.8\ radians=1.8\times 57.3\textdegree\\\\1.8\ radians=103.14\textdegree$

As we know the formula for "Length of an arc":

$\text{Length of an arc}=\frac{\theta}{360\textdegree}\times 2\pi r\\\\10.8=\frac{103.14}{360\textdegree}\times 2\times \frac{22}{7}\times r\\\\10.8=1.8r\\\\r=\frac{10.8}{1.8}\\\\r=6$

Hence, Length of the radius of the sector is 6 units.