Question

What is the circumference of a circle with an area of 81 in2?

Answer 1

find the radius first.

Answer 2

circumference is 2pi(r)
and 2pi(r)^2 is the area.

so to find r just take 2pi(r)^2 = 81
and solve for r and then plug that into the equation of the circumference

Answer 3

i still dont see it

Answer 4

they give you the area and already and you need to convert it into a circumference.
looking at the equation of the circumference of a circle:\[2\pi r\] and area \[2\pi r^2\]you can see that they are related by r

Answer 5

right.. so i dont understand what i need to do now

Answer 6

in the problem they already tell you that the area is 81

Answer 7

so they already give you \[\pi r^2 = 81\]

Answer 8

oh ok so the radius is 9?

Answer 9

then to solve for r, you divide both sides by pi to get\[\pi r^2=81/ \pi\]

Answer 10

whoops

Answer 11

\[ r^2 = 81/ \pi\]

Answer 12

you need to watch you algebra and follow the order of operations ->PEMDAS

Answer 13

then take the square root of both sides to get\[r=\sqrt{81/ \pi}\]

Answer 14

remember that pi is a number (like 3.1415 something) so its treated like it is\[ (3.14)\times \pi = 81\]

Answer 15

you can check if your r is correct by plugging it into the equation of the area and you should get 81

then by the equation of the circumference and the r that we found we get that the circumference is \[2 \pi \sqrt{81/\pi} \] or if you simplify \[18 \pi^{1/2}\]

Answer 16

i whoops i mean (3.14) x r = 81 not (3.14) x pi = 81

Answer 17

Circumference is \[2\pi*r\]
Area is \[\pi*r^2\]
So the question gives you that the Area of the Circle is 81.
Plug 81 into the Area formula.
\[81=\pi*r^2\]
From this equation you can solve and get r.
So do the math and r=5.07

Now we have the value of the radius r=5.07
We now can solve for the circumference
\[Circumference=2\pi*r\]
\[Circumference=2\pi*(5.07)\]

Do the math and your answer is 31.85 in^2