Question

From a circle of radius 7 cm the largest possible square is cut and removed Find the area of the remaining portion (in cm${}^2$)

• A. 48
• B. 50
• C. 54
• D. 56

Answer 1

The correct option is D 56

From the figure, $AC$ & $BD$ are the diameter of the circle & $ABCD$ be the square.

The diagonal of the largest square will be equal to the diameter of the circle.
So, Diagonal of the square $=2\times 7=14cm$ i.e. $AC=BD=14$ $cm$

Clearly from the figure, triangle $ABC$ is a right angled triangle, so using pythagoras we can find the sides of square i. e. $(AC{)}^2=(AB{)}^2+(BC{)}^2$

$\therefore \sqrt{2}\times side=14cm$
$=>Side=7\sqrt{2}cm$
Now, area of remaining portion $=$ Area of circle $-$ Area of square $=\pi \times radiu{s}^2-sid{e}^2$
$=\frac{22}{7}\times 7^2-(7\sqrt{2}{)}^2=154-98=56c{m}^2$