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Question

The area of the square inscribed in a semicircle is 2 cm2. If the semi-circle is extended to a full circle, the area of the square inscribed in this circle is


A

6 cm2

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B

7 cm2

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C

4 cm2

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D

5 cm2

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Solution

The correct option is D

5 cm2



Area of square = 2cm2

Side of square = 2cm

Let r be the radius of the semicircle.

Then from the figure,

r2=(2)2+(22)2

r2=2+(24)

r2=52

r=(52)

When the semicircle is extended to form a full circle, the diagonal of the square inscribed in it will be the diameter of the circle.

r=(52)

So, diameter =2×(52)

Diagonal of square =side×2

side×2=2×(52)

side×2=2×5

side=5

Area of square =side2

Area =(5)2

=5 cm2


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