## anonymous one year ago *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

1. anonymous

ooh a medal!

2. anonymous

Yes a medal

3. anonymous

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

4. anonymous

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

5. anonymous

Cool

6. anonymous

the area comes with the square of the radius

7. anonymous

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

8. anonymous

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

9. anonymous

no

10. 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

11. anonymous

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

12. anonymous

So the area is 3?

13. anonymous

smaller has area 3 yes

14. anonymous

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

15. anonymous

so is it A?`

16. anonymous

no

17. anonymous

c?

18. anonymous

yes

19. anonymous

you want to take half a minute i can explain easy

20. anonymous

Okay thanks so much! That would be a big help

21. 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

22. anonymous

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

23. anonymous

And the little one is 48

24. anonymous

the ratio of the sides is $$3:1$$ but the ratio of the areas is $$144:16=9:1$$

25. anonymous

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

26. 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

27. anonymous

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

28. anonymous

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

29. 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

30. anonymous

so if the ratio of the sides is say $$5:2$$ then the ratio of the areas is $$25:4$$

31. anonymous

Oh wow that makes so much more sense now

32. anonymous

33. anonymous

34. anonymous

Yes of course!

35. anonymous