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Question

A semi-circle is inscribed in a quarter circle as shown in the figure,

What fraction of the quarter circle is shaded ?

A
13
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B
23
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C
34
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D
35
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Solution

The correct option is B 23
Let the radius of quarter circle be R and semicircle be r
Area fraction can be written as,
Area of semi-circle A1=12πr2
Area quarter circle A2=14πR2
A1A2=2r2R2
Constructing a square as OACD as shown,

using Pythagoras theorem in OCE
R2=r2+(r2)2R2=3r2

Hence the ratio will be
A1A2=23

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