Question

In a circle an arc length 10 is intercepted by a central angle of 2/3 radius

Answer 1

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.

$l=r\theta$, where,

$l$ = Arc length,

$r$ = Radius,

$\theta$ = Central angle corresponding to arc length.

Upon substituting our given values in arc-length formula, we will get:

$10=r\cdot \frac{2}{3}$

$10\cdot \frac{3}{2}=r\cdot \frac{2}{3}\cdot \frac{3}{2}$

$5\cdot \frac{3}{1}=r$

$15=r$

Therefore, the radius of the given circle would be 15 units.