Question

*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

Answer 1

ooh a medal!

Answer 2

Yes a medal

Answer 3

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

Answer 4

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

Answer 5

Cool

Answer 6

the area comes with the square of the radius

Answer 7

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

Answer 8

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

Answer 9

no

Answer 10

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

Answer 11

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

Answer 12

So the area is 3?

Answer 13

smaller has area 3 yes

Answer 14

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

Answer 15

so is it A?`

Answer 16

no

Answer 17

c?

Answer 18

yes

Answer 19

you want to take half a minute i can explain easy

Answer 20

Okay thanks so much! That would be a big help

Answer 21

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

Answer 22

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

Answer 23

And the little one is 48

Answer 24

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

Answer 25

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

Answer 26

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

Answer 27

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

Answer 28

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

Answer 29

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

Answer 30

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

Answer 31

Oh wow that makes so much more sense now

Answer 32

glad to help
you got another one we can try ?

Answer 33

I was just about to ask you too Lol!

Answer 34

Yes of course!

Answer 35

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

Answer 36

Alright I sure will