Question

Find the radius of a circle on which a central angle measuring 5pie/ 6 radians intercepts an arc on the circle with a length of 35 pie cm.

Answer 1

Given the central angle (say ∡AOB), ∅ =
`(5\pi)/(6)`

Arc length by the same central angle, s = 35π cm.

We know the formula for Arc Length is given by :-

Arc Length = Central angle × Radius

s = ∅ · r

`35\pi =((5\pi)/(6)) \;r\\\\ r = (35\pi)/((5\pi)/(6)) = ((35\pi)/(1)) ((6)/(5\pi)) =(7)(6)=42\;cm`

So, radius of circle is 42 cm.