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Question

If a wire is bent into the shape of a square, then the area enclosed by the square is 81cm2. When the same wire is bent into a semi-circular shape, then the area enclosed by the semi circle will be

A
81cm2
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B
44cm2
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C
77cm2
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D
154cm2
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Solution

The correct option is C 77cm2
Let the side of the square be a cm.
Now, area of square=a2
81=a2a=9cm
Now, length of wire=4×a
=4×9
=36cm
Perimeter of semicircular wire=πr+2r
Also, perimeter of Semicircular wire=Length of wire
πr+2r=36
r(227+2)=36
367×r=36
r=7cm
Area of semicircular shape=12×πr2
=12×227×7×7
=77cm2

908430_83577_ans_3a1784353655418d91b47a37da0ac7c9.PNG

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