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

The exact circumference of a circle is,
`12√(\pi)` inches

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;

`(36)/(\pi) = r^2`

or

`r^2=(36)/(\pi)`

⇒
`r =\sqrt{(36)/(\pi)}`

⇒
`r = (6)/(√(\pi))`

We have to find the exact circumference of a circle.

`C = 2 \pi r`

then;

`C = 2 \cdot \pi \cdot (6)/(√(\pi)) = 12 \cdot √(\pi)`

⇒
`C = 12√(\pi)` inches

Therefore, the exact circumference of a circle is,
`12√(\pi)` inches