Question

Calculate the length of an arc of a circle, radius 21m, which

subtends an angle of 600 at the centre of the circle. (Take TT=22/7)
(A) 0.22m (B) lim (C) 22m (D) 2.31m (E) 23.1m
​

Answer 1

I'm guessing the angle is supposed to have measure 60º, not 600º... In this case,

`\frac\ell{2\pi(21\,\mathrm m)}=(60^\circ)/(360^\circ)`

That is, the length of the arc we care about
`(\ell)` occurs with the circle's circumference in the same ratio as the measure of the central angle it subtends occurs with one complete revolution of the circle. Then with
`\pi=\frac{22}7`, we have

`\frac\ell{132\,\rm m}=\frac16\implies\ell=22\,\mathrm m`

so the answer is C.