Question

A square, with an area of $40$, is inscribed in a semicircle. The area of a square that could be inscribed in the entire circle with the same radius, is:

• A. $80$
• B. $100$
• C. $120$
• D. $160$
• E. $200$

Answer 1

The correct option is B $100$

Area of square$=40$

Side of square$=\sqrt{40}=2\sqrt{10}$

Let r be the radius of semi circle, then

$r^2={\left(2\sqrt{10}\right)}^2+{\left(\frac{2\sqrt{10}}{2}\right)}^2=40+10=50$

$\Rightarrow r=\sqrt{50}=5\sqrt{2}$

In a full square the diagonal of square will be the diameter of circle.

$\therefore D=2r=10\sqrt{2}$

$\therefore$ Side of square$=\frac{Diagonal}{\sqrt{2}}=\frac{10\sqrt{2}}{\sqrt{2}}=10$

Area of square$={\left(10\right)}^2=100$