Question

The area of a square inscribed a circle with radius $14cm$ is ............ ${cm}^2$

• A. 392
• B. 784
• C. 196
• D. 98

Answer 1

Answer: (A)

392

When a square of side $a$ is inscribed in a circle of radius $r$,

the diameter of the circle is equal to the length of diagonal of the square

diameter = $2r$

$\Rightarrow 2r=\sqrt{2}a$

$\Rightarrow a=\sqrt{2}r$

$a$ is the length of a side of the square

$r$ is the radius of the circle

given , $r=14cm$

$\Rightarrow a=\sqrt{2}\times 14=14\sqrt{2}cm$

Area of the square $={\left(side\right)}^2=a^2={\left(14\sqrt{2}\right)}^2=196\times 2=392c{m}^2$