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