Answer:
The exact circumference of a circle is, [tex]12\sqrt{\pi}[/tex] inches
Step-by-step explanation:
Area(A) and circumference(C) of the circle is given by:
[tex]A = \pi r^2[/tex]
[tex]C = 2 \pi r[/tex]
where, r is the radius of the circle.
As per the statement:
an area equal to 36 sq. in.
⇒A = 36 sq. in.
then;
[tex]36 = \pi r^2[/tex]
Divide both sides by [tex]\pi[/tex] we have;
[tex]\frac{36}{\pi} = r^2[/tex]
or
[tex]r^2=\frac{36}{\pi}[/tex]
⇒[tex]r =\sqrt{\frac{36}{\pi}}[/tex]
⇒[tex]r = \frac{6}{\sqrt{\pi}}[/tex]
We have to find the exact circumference of a circle.
[tex]C = 2 \pi r[/tex]
then;
[tex]C = 2 \cdot \pi \cdot \frac{6}{\sqrt{\pi}} = 12 \cdot \sqrt{\pi}[/tex]
⇒[tex]C = 12\sqrt{\pi}[/tex] inches
Therefore, the exact circumference of a circle is, [tex]12\sqrt{\pi}[/tex] inches
