Question

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

1) 12
2) 18
3) 324

Answer 1

The answer would be option 1) 12

Answer 2

The circumference is
`C=12√(\pi )\:in`.

Explanation:

The area of a circle when we know the circumference is

`A=(C^2)/(4\pi )`

We know the area
`A=36 \:{in^2}`, we plug this value into the above equation and we solve for C the circumference.

`36=(C^2)/(4\pi )\\(C^2)/(4\pi )=36\\(C^2\cdot \:4\pi )/(4\pi )=36\cdot \:4\pi \\\\C^2=144\pi \\C=√(144\pi )\\C=12√(\pi )`

The circumference is
`C=12√(\pi )\:in`.