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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.

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aachen

Given the central angle (say ∡AOB), ∅ = [tex] \frac{5\pi}{6} [/tex]

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

[tex] 35\pi =(\frac{5\pi}{6}) \;r\\\\ r = \frac{35\pi}{\frac{5\pi}{6}} = (\frac{35\pi}{1}) (\frac{6}{5\pi}) =(7)(6)=42\;cm [/tex]

So, radius of circle is 42 cm.