Find the exact circumference of a circle with an area equal to 36 sq. in.
a. 12 pi
b. 18 pi
c. 324 pi

- anonymous

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- anonymous

12 Pi

- anonymous

How do you find the radius from this info? Or lack thereof

- jim_thompson5910

A = pi*r^2
36 = 3.14*r^2
solve for r to get r = ???
once you know the value of r, you can find the circumference C
C = 2*pi*r

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- anonymous

But how do you find R? Thats where Im stuck

- anonymous

the question wants the circumference function in pi... so we can get the relation

- jim_thompson5910

did you divide both sides of 36 = 3.14*r^2 by 3.14 ?

- anonymous

No.

- jim_thompson5910

what do you get when you do so

- anonymous

Well 36/3.14 is 11.46

- jim_thompson5910

now if r^2 = 11.46, then what must r be?

- anonymous

What does ^ mean?

- jim_thompson5910

r^2 means r squared

- jim_thompson5910

r^2 = r*r

- jim_thompson5910

for example, 5^2 = 5*5 = 25

- anonymous

So multiply 11.46 by 11.46?

- anonymous

Wait, no. 5.73 multiplies by 5.73?

- anonymous

Multiplied?

- jim_thompson5910

some number, multiplied by itself, gives 11.46

- jim_thompson5910

to find this number, you take the square root of 11.46

- jim_thompson5910

it turns out that
sqrt(11.46) = 3.385 roughly
which means 3.385*3.385 = 11.458225, pretty close to 11.46

- anonymous

So then i have 36=3.14*3.38^2?

- jim_thompson5910

now use that r value to find the circumference C
use C = 2*pi*r

- anonymous

So two times pi times 3.38?

- jim_thompson5910

2 times pi times 3.38

- jim_thompson5910

oh sry didn't see your two, nvm

- jim_thompson5910

yes you are correct

- anonymous

21.23 is what I got.

- jim_thompson5910

Question: does the original "36" given in the problem also have a "pi" attached to it?

- anonymous

Yes

- jim_thompson5910

ok so that changes things a bit

- anonymous

Sorry.

- jim_thompson5910

if the area is A = 36pi, then
A = pi*r^2
36pi = pi*r^2
36 = r^2 ... the pi terms cancel
if r^2 = 36, then r = ??

- anonymous

6?

- jim_thompson5910

yes, then you plug that into C = 2*pi*r

- anonymous

37.69?

- jim_thompson5910

notice how each answer has a 'pi' in it
so ignore the pi for now
compute 2*r and then tack on 'pi' at the end

- jim_thompson5910

example: if r = 7, then 2*pi*r = 14pi

- anonymous

Im still getting the same thing.

- jim_thompson5910

you should get 12pi

- anonymous

2 times R which is 6 means 12.
Then 12*pi. The answer I'm getting is still 37.69

- jim_thompson5910

2*r = 2*6 = 12

- jim_thompson5910

you leave it as 12pi

- anonymous

OH! Okay.

- anonymous

Thank you so much! Sorry I am so bad at this!

- jim_thompson5910

whenever you see the key term "exact" that means to leave the 'pi's as they are

- jim_thompson5910

you did good

- anonymous

Oh. Sounds good.
Thank you that means a lot!

- jim_thompson5910

you're welcome

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