The difference in area between the circle and the square is [tex]4\pi -8[/tex]
Step-by-step explanation:
Step 1: Finding the area of the square
The area of the square = [tex]side ^2[/tex]
Here the side of the square = [tex]2\sqrt{2}[/tex]
The area of the square = [tex](2\sqrt{2})^2[/tex]
The area of the square = 8 square units...............(1)
Step 2: Finding the area of the circle
To find the area of the circle lets find the diagonal of the square
The diagonal of the square is equal the diameter of the circle
Now the diagonal of the square =[tex]( \sqrt{2})(side)[/tex]
Thus substituting the value
The diagonal = [tex]( \sqrt{2})(2 \sqrt{2})[/tex] = 4 units
[tex]\therefore[/tex]Diameter of the circle = 4 units
Now the area of the circle =[tex]\pi r^2[/tex]
where r is the radius of the circle
r = [tex]\frac{diameter}{2}[/tex] =[tex]\frac{4}{2}[/tex] = 2 units
Thus the area of the circle = [tex]\pi (2)^2[/tex]= [tex]4 \pi[/tex] square units .....................(2)
Step 3: Finding the difference
Difference = area of the circle - area of the square
From (1) and (2)
Difference =[tex]4\pi - 8[/tex] square units
