Question

A circle of maximum possible size is cut from a square sheet of board. Subsequently, a square of maximum possible size is cut from the resultant circle. What will be the area of the final square?

• A. $\frac{3}{4}$ of the original square
• B. $\frac{1}{2}$ of the original square
• C. $\frac{1}{4}$ of the original square
• D. $\frac{2}{3}$ of the original square.

Answer 1

The correct option is B

$\frac{1}{2}$ of the original square

Step 1: Find area of square

Let $a$ be the side of the square sheet

Thus, the area of the bigger square sheet $=a^2$ ……..(1)

Step 2: Find diameter of circle

Now, the circle of maximum possible size from it is, given as:

The radius of the circle$=\frac{a}{2}$

Then the diameter$=a$

Step 3: Find area of smaller square

We know that, any square in the circle of maximum size should have the length of the diagonal which is equal to the diameter of the circle.

It means that, the diagonal of a square formed inside a circle is “$a$”.

Hence, the square side $=\frac{a}{\sqrt{2}}$

Thus, the area of square$=\frac{a^2}{2}$ …..(2)

By equating the equations (1) and (2), we will get

Area of the resultant square is $\frac{1}{2}$ of the original square.

Hence, option B is the correct option.