A semi-circle of diameter 1 unit sits at the top of a semi-circle of diameter2 units. The shaded region inside the smaller semi-cricle but outside the larger semi-circle a lune. The area of the lune is-

Options

A. `pi/6-(sqrt3)/4`
B. `(sqrt3)/4-pi24`
C. `(sqrt3)/4-pi/12`
D. `(sqrt3)/4-pi/8`

Answer

B

Explanation

`"Requireda area "=(pi(1/2)^(2))/2-((60^(@))/(360^(@))xxpi(1)^(2)-(sqrt3)/4xx1^(2))`
`=pi/8-(pi/6-(sqrt3)/4)=(sqrt3)/4-pi/24`