## ryuu 2 years ago The volume of a can is 28.3 cubic inches (in.^3). If the radius and the height of the can are multiplied by a scale factor of 2, what is the volume of the new can?

1. ryuu

Please tell me how you got to the answer, this kind of material will be in my test tomorrow.. x.x

2. Dido525

What kind of can? I assume it is is a Cylinder but...

3. ryuu

It just says that, so I would assume it's a cylinder. =P

4. ryuu

So yeah lol

5. Dido525

Well the volume of a cylinder is pi*r^2*h.

6. Dido525

When something is multiplied by a factor you replace the ariable by that same factor.

7. ryuu

So... replace r with 2, that's all?

8. Dido525

And h. Do you understand why?

9. ryuu

ahh sorry word problems get me. No I don't.

10. Dido525

When you scale something or multiplying by a factor you are basically saying "two times more than the original value" .

11. Dido525

Does that make sense?

12. Dido525

So when I say I multiply by a factor of 5 I am basically saying "Take your original value and multiply by 5"

13. ryuu

Somewhat. So in some case, just guessing, it'd be like half of the original amount given? 28.3? or... x.x; lol I mean I get I have to replace it and why now

14. Dido525

Or for instance, when I say I multiply something by a factor of 7 I am saying "Take your original number and replace it by 7 times the original value" .

15. ryuu

I got 25.12 just now.

16. ryuu

So, basically when multiplying by a factor, you replace the other numbers? in this case the radius and the height?

17. Dido525

Yeah. Replace it by whatever factor times that number.

18. ryuu

so 25.12 would be wrong i suppose haha.. xD?

19. ryuu

Sorry.. I learned this all before, but since it's a new teacher he shows us in a different way, and it's getting me all confused.. :/

20. Dido525

Well The volume is directly proportional to the height and the radius squared. So If you increases the radius and height by a certain factor the Volume increases by the same factor.

21. Dido525

Does that make sense?

22. ryuu

honestly? still kinda lost. :|

23. Dido525

Okay. Tell me what you don't understand.

24. ryuu

|dw:1359091358356:dw|

25. ryuu

2 > r / h lol

26. Dido525

No.... :P .

27. ryuu

the thing i dont get is.. i get lost after they say the radius and height of the can are multiplied by the factor of 2

28. ryuu

blehh xD

29. ryuu

and i know 28.3 is the volume of the can

30. ryuu

but im confused if ill need to use 28.3 # at all or just work out a certain equation like you said replace with the other things in my case i think this: 3.14(2)^2(2)

31. Dido525

Yeah you will use the 28.3

32. Dido525

Here Maybe a picture will help.

33. ryuu

kk

34. Dido525

|dw:1359091625314:dw|

35. ryuu

oh i see, but.. then what's the radius? o.o

36. Dido525

|dw:1359091742557:dw|

37. Dido525

That's a badly drawn r XD .

38. ryuu

XD! It's okay I understand. And I appreciate the help thanks a lot. i got a test tomorrow.. ><

39. ryuu

and that teacher teaching his ways just gets me confused all the time, i mostly teach myself instead xD

40. Dido525

Did you understand me though?

41. ryuu

somewhat, im confused as to what happened to r and pi though xD

42. ryuu

and why group in the replaced 2 with the r if you'll be replacing it?

43. Dido525

The pi is still there. I replaced the radius with 2r because we are multiplying the radius by a factor of 2.

44. ryuu

so pretty much just leave the r alone, and just leave it aside and continue the problem?

45. ryuu

as well as with pi? and just multiply the new factors 8 and 28.3

46. ryuu

right?

47. Dido525

No... :P . Rather replace the r by 2r because we are multiplying the r by a factor of 2 and then square the resultant.

48. ryuu

oh i see. ok, but that doesn't explain why pi is practically gone lol

49. Dido525

No no. The pi is there. We can't multiply pi by a factor because pi is a fixed, constant number.

50. ryuu

ohh okay.

51. Dido525

Does that make sense?

52. ryuu

yes. thank you. xD

53. ryuu

sorry if i got you frustrated haha.. =X

54. Dido525

Nope :) .

55. ryuu

:D

56. ryuu

can ya help me with another one? similar stuff just finding the area of complex and irregular figures

57. Dido525

Erm... Maybe.

58. ryuu

dont gotta lol just asking if you can or want to.

59. Dido525

No I mean, I might not be able to solve it.

60. Dido525

61. ryuu

Oh , kk, uhm it's just algebra all the same. here it goes. A rectangular mirror is 24 inches by 48inches. The frame around the mirror is 3inches. wide. Find the area of the mirror including the frame.

62. ryuu

I multiplied 24 and 48 and got 1,152 but that would just be the mirror's area. I also need the frames

63. Dido525

Did you draw a picture?

64. ryuu

Mhm. I shaded the frame to make it look differently. But i also tried multiplying all numbers and it doesn't add up

65. ryuu

and i get a bit confused sometimes with this book with the problems cause sometimes they're 3 dimensional lol

66. ryuu

and i mix up as to where to put the numbers on what side or what not

67. ryuu

idk if im just messing myself up honestly haha

68. Dido525

69. ryuu

like i said i got 1152 lol

70. Dido525

I think it's 1,620 inches ^2 .

71. ryuu

dunno what i missed

72. Dido525

Here look at this picture.

73. Dido525

|dw:1359093139215:dw|

74. Dido525

|dw:1359093195504:dw|

75. ryuu

So you're sharing all 3s down the middle? and breaking em down? to add 6 to both 24 and 48?

76. Dido525

yeah because we are given the frame is 3 inches wide right? So it's 3 inches wide everywhere. Does that make sense?

77. ryuu

yes it does thank you very much, once again. :)

78. Dido525

Welcome!

79. ryuu

time to finish hw, bye, take care and i fan'd ya. :P