*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

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*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

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

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Other answers:

i am trying to get all the medals i can so i can trade in my bike for a kia sedona
Cool
the area comes with the square of the radius
so it the ratio of the radius is 3 : 1 the ratio of the area is \(3^2:1\) i.e. \(9:1\)
Oh. I thought you were supposed to divide 27 by 3 and get 9?
no
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
if the larger circle has area 27, then the smaller one has areas one-ninth as large \[\frac{27}{9}\]
So the area is 3?
smaller has area 3 yes
Btw the answers are a) 9pi b) 6pi c) 3pi
so is it A?`
no
c?
yes
you want to take half a minute i can explain easy
Okay thanks so much! That would be a big help
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
now suppose you have another square whose sides is 3 times as large, so sides is12 the area of that square is \(12^2=144\)
And the little one is 48
the ratio of the sides is \(3:1\) but the ratio of the areas is \(144:16=9:1\)
in other words, the ratio of the areas is the square of the ratio of the sides
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
same with the circle ratio of radii 3:1 ratio of area 9:1
So sides and areas will always be different? I think that's where I had went wrong
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
so if the ratio of the sides is say \(5:2\) then the ratio of the areas is \(25:4\)
Oh wow that makes so much more sense now
glad to help you got another one we can try ?
I was just about to ask you too Lol!
Yes of course!
go ahead i will take a look, but first give me your answer
Alright I sure will

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