Question

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

• A. 1:2
• B. 2:3
• C. 2:5
• D. 3:4
• E. 3:5

Answer 1

The correct option is C 2:5

Let side of square $=a$

& radii of circle $=r$

$(b=a/2)$

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

Area of square $=a^2=\frac{{4r}^2}{5}$

Semicircle

$a^2={2r}^2$

$\frac{Ar.ofsq}{Ar.ofcircle}=\frac{a^2}{{\pi r}^2}=\frac{{2a}^2}{{\pi a}^2}=\frac{2}{\pi }$

Ar of ${\left(square\right)}_{circle}=a^2={2r}^2$

Ratio $\to \frac{{4r}^2}{5\times 2r^2}=\frac{2}{5}$