We have been given that in a circle an arc length 10 is intercepted by a central angle of 2/3. We are supposed to find the radius of the circle.
We will use arc-length formula to solve our given problem.
[tex]l=r\theta[/tex], where,
[tex]l[/tex] = Arc length,
[tex]r[/tex] = Radius,
[tex]\theta[/tex] = Central angle corresponding to arc length.
Upon substituting our given values in arc-length formula, we will get:
[tex]10=r\cdot \frac{2}{3}[/tex]
[tex]10\cdot \frac{3}{2}=r\cdot \frac{2}{3}\cdot \frac{3}{2}[/tex]
[tex]5\cdot \frac{3}{1}=r[/tex]
[tex]15=r[/tex]
Therefore, the radius of the given circle would be 15 units.
