In a circle of radius `21` cm, an arc subtends an angle of `60^@` at the centre. Find:
(i) the length of the arc
(ii) area of the sector formed by the arc
(iii) area of the segment formed by the corresponding chord.

Answer

(i) `7pi` cm (ii) `231` `cm^2` (iii) `40.04` `cm^2`

Explanation

(i) We know `60^@=pi/3`

Length of arc `=pi/3xx21=7picm`
(ii) Area of the sector `=60^@/360^@xxpi(21)^2=(22xx21xx21)/(6xx7)=231cm^2`
(iii) Area of segment = area of sector AOB - Area of triangle AOB
`=231-sqrt3/4xx21^21=40.04cm^2`