Answer:
d = 52 in
C = 6π mm²
Step-by-step explanation:
The formula of a circumference:
[tex]C=2\pi r=d\pi[/tex]
r - radius
d - diameter
We have [tex]C=52\pi\ in[/tex].
Calculate the diameter using [tex]C=d\pi[/tex]:
[tex]d\pi=52\pi[/tex] divide both sides by π
[tex]d=52\ in[/tex]
-------------------------------------------------------------------------
If a circle inscribed in a square, then the diameter of a circle and a side of a square are congruent (have the same length).
We have the area of the square:
[tex]A=36\ mm^2[/tex]
The formula of an area of a square:
[tex]A=s^2[/tex]
s - side
Substitute:
[tex]s^2=36\to s=\sqrt{36}\\\\s=6\ mm[/tex]
The formula of a circumference [tex]C=d\pi[/tex]
d - diameter
d = s → d = 6 mm
Substitute:
[tex]C=6\pi\ mm[/tex]
