Question

A circle has an area twice that of a square. Find the ratio of the circumference of the circle to the perimeter of the square.

Answer 1

squaring the circle are we ..

Answer 2

so a ratio of perimeters ....

Answer 3

I don't even know where to start. I mean, I could obviously guess and check, but I wanted to know how to do it algebraically.

Answer 4

Sa = s^2

Ca = pi r^2 = 2Sa = 2s^2

so far

Answer 5

25a?

Answer 6

Oh, 2Sa

Answer 7

sorry

Answer 8

4s = perimeter square

2pi r = perimeter of a circle

pi r^2 = 2s^2 is a good relationship to figure out the rest

Answer 9

prolly get things in terms of s

Answer 10

sqrt(pir^2/2) = s

Answer 11

r = sqrt(2s^2/pi)

Answer 12

where from there?

Answer 13

so depending on what variable youwant this to speak in:

4s : 2pi r

and then simplify is my best guess

Answer 14

apply them to the perimeter equations then square it?

Answer 15

a ratio is just how one thing looks next to another; proportions and fractions and the like

Answer 16

yes
2pisqrt(2s^2/pi)
:
4sqrt(pir^2/2)

Answer 17

ima square both sides

Answer 18

get them speaking the same variable; not 2 different variables

Answer 19

how?

Answer 20

by solving for s or r from the relationship itself; pick on of them and go with it :)

Answer 21

but all we have so far is the area and perimeter formulae

Answer 22

and how r and s are related

pi r^2 = 2s^2

Answer 23

the area of the circles is two times that of the area of the square

Answer 24

you're gonna have to do all of this I'm not following

Answer 25

ok, heres my thoughts

area square = s^2

area circle = pi r^2

right?

Answer 26

yes

Answer 27

area circle = 2 times area square

pi r^2 = 2s^2

right?

Answer 28

yes

Answer 29

good, solve for say ... r in terms of s

Answer 30

r = sqrt(2s^2/pi)

Answer 31

pi r^2 = 2s^2

r^2 = 2s^2 /pi

r = s sqrt(2/pi)

Answer 32

now; perimeter of a square is: 4s

perimeter of a circle is: 2pi r

right?

Answer 33

yes

Answer 34

so the ratio of circle to square is then

4s : 2pi r

or simply

s = pi r

now sub in for r

Answer 35

not s = ... but typos persist

Answer 36

?

Answer 37

s = pi r?

Answer 38

wouldnt it be 2s = pi r?

Answer 39

so the ratio of circle to square is then

4s : 2pi r

or simply

s : pi r

now sub in for r ; we know r = s sqrt(2/pi)

s : s pi sqrt(2/pi)

divide off the s

1 : pi sqrt(2/pi)

Answer 40

like i said, typos persist :)

Answer 41

what do you mean by that?
sorry I was away for a couple of minutes, the site was doing weird stuff

Answer 42

yeah, its freezing up on my end too

Answer 43

"typos persist" whhat do you mean by that?

Answer 44

i mean that you have to read thru the errors that pop up from trying to type on a keyboard ...

Answer 45

so will you please fix that whole post, (your fourth to last)

Answer 46

so the ratio of circle to square is then

4s : 2pi r

or simply

s : pi r

now sub in for r ; we know r = s sqrt(2/pi)

s : s pi sqrt(2/pi)

divide off the s

1 : pi sqrt(2/pi)

we can push the pi inside by ^2ing it

1 : sqrt(2pi^2/pi)

1 : sqrt(2 pi)

and thats about it

Answer 47

s : pi r
you did it again

Answer 48

alright, I still dont understand what your typo problem was... however you did get the answer for your typo, and Now I can just do sqrt(2pi) : 2

Answer 49

lol .... yeah :)

Answer 50

4/2 = 2 not 1 ... i really should try to sleep ;)

Answer 51

That's probably a good idea