The area of a square inscribed in a semicircle is to the area of the square inscribed in the entire circle as

Let side of square inscribed in the semi circle be $$a$$ cm and radius of semi circle = $$r$$ cm

In right $$\triangle$$, => $$r^2=a^2+(\frac{a}{2})^2$$

=> $$r^2=a^2+\frac{a^2}{4}$$

=> $$r^2=\frac{5a^2}{4}$$

=> $$a^2=\frac{4r^2}{5}$$ --------------(i)

Similarly, let side of another square be $$b$$ cm and radius of same circle = $$r$$ cm

=> $$b^2+b^2=(2r)^2$$

=> $$b^2=2r^2$$ --------------(ii)

$$\therefore$$ Ratio of area of first square to area of second square = $$\frac{a^2}{b^2}$$

Substituting values from equation (i) and (ii), => $$\frac{\frac{4r^2}{5}}{2r^2}$$

= $$2:5$$

=> Ans - (C)