Question

The area of circle which encloses a square of side 10 cm is

• A. $25\pi$
• B. $50\pi$
• C. $75\pi$
• D. $100\pi$

Answer 1

The correct option is B

$50\pi$

Let ABCD be the square of side 10 cm

Now, in right angled triangle ABC we have

$A{B}^2+B{C}^2=A{C}^2,\text{AC being the diagnol.}$

$A{C}^2={10}^2+{10}^2\Rightarrow A{C}^2=200\Rightarrow AC=10\sqrt{2}$

Now this AC is diameter of the circle

So $Diameter=10\sqrt{2}$

$2r=10\sqrt{2}\Rightarrow r=5\sqrt{2}$

radius of circle is $5\sqrt{2}$ as

Area of circle will be $\pi r^2=\pi (5\sqrt{2}{)}^2$

= $50\pi c{m}^2$