Question

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

Answer 1

if the side lengths are 2sqrt(2), then the radius is 2 (by the pythagorean theorem) so the circle has an area of 4π, and the circle has a radius of 8. so the difference would be 4π-8.

Answer 2

If the side of the square is 2*sqrt(2), then the diagonal of the square is


a^2+b^2 = c^2

(2*sqrt(2))^2 + (2*sqrt(2))^2 = c^2

8 + 8 = c^2

16 = c^2

16 = c^2

c^2 = 16

c = 4

So the diagonal is 4. This means that the radius of the circle is 2


The area of the square is then

A = s^2

A = (2*sqrt(2))^2

A = 8

and the area of the circle is

A = pi*r^2

A = pi*2^2

A = 4pi

Therefore, the difference between the two areas is then

(Area of the Circle) - (Area of the Square)

4pi - 8