Question

Find the exact circumference of a circle with an area equal to 36 sq. in.

Answer 1

The area of the circle is determined through the equation,
                                     A = πr²
Plug in the value of area
                                    36 in² = πr²       ;  r = 3.385 in
The formula for the circumference of the circle is,
                                    C = 2πr
Substitute the value of radius,
                                C = 2π(3.385 in) = 6.77π in
Thus, the circumference of the circle is 6.77π inches. 

Answer 2

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