The area of a circle is 81π m². What is the circumference, in meters? Express your answer in terms of π.

Question

asked Dec 10, 2021 221k views

2 Answers

Hatem Alimam · Answer 1 · 2021-12-17T16:12:52+0000

Answer:

$18\pi m$

Explanation:

to find the circumference we need to find the radius of the circle.

For this, we use the formula for the area :

$a=\pi r^2$

where
is the area,
$\pi$ is a constant
$\pi =3.1416$ and
is the radius.

we know that the area is:

$a=81\pi m^2$

so we substitue this into the previous formula:

$81\pi m^2=\pi r^2$

and we solve for
:

$(81\pi m^2)/(\pi )=r^2\\ \\81m^2=r^2\\\\√(81m^2)=r\\\\9m=r$

the radius is 9 meters.

Now we use the formula for circumference of a circle:

$C=2 \pi r$

and substitute the value that we've just found for r:

$C=2\pi (9m)\\C=18\pi m$

the answer in terms of
$\pi$ is
$18\pi$ meters is the circumference