Question

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 i


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Answer 1

Answer:

=√3/4-π/24

Explanation:

Area of the lune = Area of the smaller semicircle - Area of the segment

Area of the segment = Area of the sector - Area of the triangle formed by intersection points and the center of bigger semicircle

Also, the triangle so formed is an equilateral triangle since all the sides are of 1 unit

∴ Area of the lune =π×  1/8  −(   60/360 ×π×1 ^2 −√ 3/4×1^ 2 )

Area of the lune =  π/8 −  π/6 +√3 /4

=√3/4-π/24

Answer 2

Explanation:

The shaded region inside the smaller semi-circle but outside the larger semi-circle is called a lune.