Question

The area of the square that can be inscribed in a circle of radius $8$ cm is :

• A. $256$ $c{m}^2$
• B. $128$ $c{m}^2$
• C. $64\sqrt{2}c{m}^2$
• D. $64$ $c{m}^2$

Answer 1

The correct option is B $128$ $c{m}^2$

Diagonal of square inscribed in a circle $=$ Diameter of circle.

Therefore, $d=8+8=16cm$

Side of square, $a=\frac{d}{\sqrt{2}}=\frac{16}{\sqrt{2}}$

Area of square $={\left(\frac{16}{\sqrt{2}}\right)}^2=\frac{256}{2}=128{cm}^2$