Question

if a biggest circle is cut from a square of side 'a' units then the remaining area in the square will be?​

Answer 1

first understand the logic of question

it is given that a biggest circle is cut from  a square

of side ""a'"  

hence by this  

area of square =a x a

                        =$a^{2}$

hence diameter of circle =a

( area of circle if radius =a /2

                                      =$\pi$$r^{2}$

                                     =22/7 x a/2 x a/2

solving this we get   11$a^{2}$/14

remaining area = $a^{2}$- 11$a^{2}$/14

by solving we get=14$a^{2}$-11$a^{2}$ /14

finally remaining area=3$a^{2}$ /14

Answer 2

Remaining area is $a^{2}(1-\frac{\pi }{4})$.

Step-by-step explanation:

Given:

Side of the square is = $a$ units

Circle with maximum radius is cut from the square.

To find: Remaining area in the square

Calculation:

The biggest circle in the given square with side $a$ will have diameter of $a$ units.

Radius of the circle :  $r=\frac{a}{2}$

Now area of square: $Area_{sq}$$= side^{2}=a^{2}$

Area of circle:

$Area_{c}=\pi r^{2} \\Area_{c} = \pi (\frac{a}{2})^{2} =\pi \frac{a^{2} }{4}$

So, the remaining area $=a^{2} -\pi \frac{a^{2} }{4} = a^{2}(1-\frac{\pi }{4})$