KVPY SA Exam 2014 Question Paper

Question : 7 of 80

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A semi-circle of diameter 1 unit sits at the top of a semicircle of diameter 2 units. The shaded region inside the smaller semi-circle but outside the larger semi-circle is called a lune. The area of the lune is

$π/6-√3/4$
$√3/4-π/24$
$√3/4-π/12$
$√3/4-π/8$

Validate

Solution:

Required area =

{π(1/2)^2}/2-(60°/360°×π(1)^2-√3/4×1^2)

=π/8-(π/6-√3/4)=√3/4-π/24

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