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

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