Find the ratio of the area inside the square but outside the circle to the area of the square in the figure.

Solution:

Area of the square = a²

Area of the circle = 𝜋r²

Let the side of the square be ‘a’. Then the area of the square is a².

Notice that this length of the square is also the length of the diameter of the circle. Therefore, radius of the circle is a/2. Hence the area of the circle is 𝜋a²/4.

Now, the required area which is outside the circle and inside the square = Area of the square - Area of the circle.

∴ Area of the square - Area of the circle = a² - 𝜋a²/4

= (4a² - 𝜋a²)/4

= a² (4 - 𝜋)/4

∴The ratio of the area inside the square but outside the circle to the area of the square

=a² (4 - 𝜋)/4 : a²

= (4 - 𝜋) : 4

Thus the required ratio is  (4 - 𝜋) : 4

Find the ratio of the area inside the square but outside the circle to the area of the square in the figure.

Summary:

The ratio of the area inside the square but outside the circle to the area of the square is (4 - 𝜋) : 4