Question

Find the difference in area between the circle and the square. Click on the answer until the correct answer is showing

Answer 1

The difference in area between the circle and the square is $4\pi -8$

Step-by-step explanation:

Step 1: Finding the area of the square

The area of the square   = $side ^2$

Here the side of the square  = $2\sqrt{2}$

The area of the square =  $(2\sqrt{2})^2$

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  =$( \sqrt{2})(side)$

Thus substituting the value

The diagonal  = $( \sqrt{2})(2 \sqrt{2})$ =  4 units

$\therefore$Diameter of the circle  =   4 units

Now the area of the circle  =$\pi r^2$

where r is the radius of the circle

r = $\frac{diameter}{2}$ =$\frac{4}{2}$ = 2  units

Thus the area of the circle = $\pi (2)^2$= $4 \pi$ square units .....................(2)

Step 3: Finding the difference

Difference  = area of the circle  - area of the square

From (1) and (2)

Difference  =$4\pi - 8$ square units