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 (2)/(3)`

`10\cdot (3)/(2)=r\cdot (2)/(3)\cdot (3)/(2)`

`5\cdot (3)/(1)=r`

`15=r`

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