In a circle of radius 14 cm, an arc subtends an angle of `120^(@)` at the centre. If `sqrt(3)=1.73` then the area of the segment of the circle is

Options

A. `120.56cm^(2)`
B. `124.63cm^(2)`
C. `118.24cm^(2)`
D. `130.57cm^(2)`

Answer

A

Explanation

ar (segment `=((pir^(2)theta)/360-r^(2) "sin"(theta)/2"cos"(theta)/2)`
`=(22/7xx14xx14xx120/360)-(14xx14xxsin60^(@)cos 60^(@))`
`=(616/3-(sqrt(3))/2xx1/2xx14xx14)cm^(2)`
`=(205.36-49xx1.73)cm^(2)`
`=(205.33-84.77)cm^(2)`
`=120.56cm^(2)`.