Answer:
[tex]\pi =3.160494[/tex]
Step-by-step explanation:
step 1
Find the area of the circle with a diameter of 9 units
we know that
The area of a circle is equal to
[tex]A=\pi r^{2}[/tex]
we have
[tex]r=9/2=4.5\ units[/tex] ----> the radius is half the diameter
substitute
[tex]A=\pi (4.5)^{2}[/tex]
[tex]A=20.25\pi\ units^2[/tex]
step 2
Find the area of a square with a side length of 8 units
we know that
The area of the square is
[tex]A=b^2[/tex]
where
b is the length side of the square
we have
[tex]b=8\ units[/tex]
substitute
[tex]A=(8)^2=64\ units^2[/tex]
step 3
Equate the areas
[tex]20.25\pi=64[/tex]
solve for [tex]\pi[/tex]
[tex]\pi =\frac{64}{20.25}=3.160494[/tex]
