Question

22. A circle is inscribed in a square. Write and simplify an expression for the ratio of the area of the square to the area of the circle. For a circle inscribed in a square, the diameter of the circle is equal to the side length of the square. (3 points)

Answer 1

let the length of each side of square is S
area of circle = S^2
as the diameter of the circle is equal to the side length of the square
thus the length of its radius become S/2
area of circle = pi (S/2)^2
can you find the ratio now??

Answer 2

let the side length of the square be x

the radius of the circle is x/2

so the ratio of areas square to circle is

\[x^2 : \pi (\frac{x}{2})^2\]

or

\[x^2 : \pi \frac{x^2}{4}\]

it can be simplified by dividing both sides of the ratio by x^2

which gives

\[1:\frac{\pi}{4}\]

hope this makes sense.

Answer 3

So basically the ratio = 4/pi