*MEDAL WILL BE AWARDED*
The radii of two circles are in the ratio of 3 to 1. Find the area of the smaller circle if the area of the larger circle is 27pi sq. in.
a) 9
b) 6
c) 3

- anonymous

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- anonymous

ooh a medal!

- anonymous

Yes a medal

- anonymous

Are you jumping around or what? It's like you're answering like 10 questions at a time! Lol!
:D

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## More answers

- anonymous

i am trying to get all the medals i can so i can trade in my bike for a kia sedona

- anonymous

Cool

- anonymous

the area comes with the square of the radius

- anonymous

so it the ratio of the radius is 3 : 1 the ratio of the area is \(3^2:1\) i.e. \(9:1\)

- anonymous

Oh. I thought you were supposed to divide 27 by 3 and get 9?

- anonymous

no

- anonymous

suppose one circle has radius 1, it has area \(\pi\)
and another one has radius 3, it has area \(9\pi\) i.e. its area is 9 times as large, not 3 times

- anonymous

if the larger circle has area 27, then the smaller one has areas one-ninth as large
\[\frac{27}{9}\]

- anonymous

So the area is 3?

- anonymous

smaller has area 3 yes

- anonymous

Btw the answers are
a) 9pi
b) 6pi
c) 3pi

- anonymous

so is it A?`

- anonymous

no

- anonymous

c?

- anonymous

yes

- anonymous

you want to take half a minute i can explain easy

- anonymous

Okay thanks so much! That would be a big help

- anonymous

lets forget about a circle just use a square
the area of a square with side \(a\) is \(a^2\) like if the side is 4 the area is 16

- anonymous

now suppose you have another square whose sides is 3 times as large, so sides is12
the area of that square is \(12^2=144\)

- anonymous

And the little one is 48

- anonymous

the ratio of the sides is \(3:1\) but the ratio of the areas is \(144:16=9:1\)

- anonymous

in other words, the ratio of the areas is the square of the ratio of the sides

- anonymous

supposed you had one square with side 1, its area is 1
another has side 3, its area is 9
ratio of sides 3:1
ratio of areas 9:1

- anonymous

same with the circle
ratio of radii 3:1
ratio of area 9:1

- anonymous

So sides and areas will always be different? I think that's where I had went wrong

- anonymous

yes the ratio of the area is the SQUARE of the ratio of the sides
this should not be too surprising because the side is measured in length (one dimensional unit like feet or meters) and the area is measured in SQUARE units, like square feet or square meters

- anonymous

so if the ratio of the sides is say \(5:2\) then the ratio of the areas is \(25:4\)

- anonymous

Oh wow that makes so much more sense now

- anonymous

glad to help
you got another one we can try ?

- anonymous

I was just about to ask you too Lol!

- anonymous

Yes of course!

- anonymous

go ahead i will take a look, but first give me your answer

- anonymous

Alright I sure will

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