Question

If a square of area $3$ square units is inscribed in a circle, then the area of the circle is

• A. $\frac{3}{2}\pi sq.cm$
• B. $9{\pi }^{2}sq.cm$
• C. $6\pi sq.cm$
• D. $\sqrt{3}\pi sq.cm$

Answer 1

The correct option is A $\frac{3}{2}\pi sq.cm$

Given, area of a square $=3$ sq.cm

Let $a$ be side of square.

$\Rightarrow$ $a^2=3$

$\Rightarrow$ $a=\sqrt{3}$ cm

Diagonal $=a\sqrt{2}$

$=\sqrt{3}\times \sqrt{2}$ cm

$=\sqrt{6}$ cm

Diameter of circle $=$ diagonal of square $=\sqrt{6}$ cm

Radius $=\frac{\sqrt{6}}{2}cm$

$\Rightarrow r=\frac{\sqrt{3}}{\sqrt{2}}cm$

$\therefore$ Area of the circle $=\pi r^2$

$=\pi \times {\left(\frac{\sqrt{3}}{\sqrt{2}}\right)}^{2}c{m}^2$

$=\frac{3}{2}\pi c{m}^2$

Hence, the area of the circle is $\frac{3}{2}\pi c{m}^2$