Question

I'm missing a step, please help.
The side lengths of two different cubes are 32 cm and 48 cm. What is the ratio of the volume of the smaller to the volume of the larger (in simplest form)? [URL=http://s790.photobucket.com/user/MoGoYo480/media/12s_zpscab69862.jpg.html][IMG]http://i790.photobucket.com/albums/yy186/MoGoYo480/12s_zpscab69862.jpg[/IMG][/URL]

Here are my choices:
4/6
2/3 -> wrong on quiz
8/27
4/9

Here's what I have so far:
32 x 32 x 32 = 32768
48 x 48 x 48 = 110592
32768 / 110592 = 0.296 (this is my answer)

Answer 1

is 37/125 one of those fractions?

Answer 2

no here are my choices:
4/6
2/3
8/27
4/9

Answer 3

37/125 is the answer. Maybe they made a mistake and just computed the ratio of one side to the other (2/3)

Answer 4

I picked 2/3 as my answer but I got it wrong. Please let me know if you can show your work so I know where I went wrong.
If you can't see the image, the first cube is 48cm and second cube is 32cm. I need to find the ratio of the volume of the smaller cube to the volume of the larger cube.
Here are my choices:
4/6
2/3 -> wrong on quiz
8/27
4/9

Answer 5

8/27=.296

Answer 6

OOOOHHHHH...but how did you know that .296 was the quotient of 8/27. Did you just try dividing each fraction until you got a match?

Answer 7

Theorem:

If two solids are similar, the cube of the scale factor of the two solids is equal to the ratio of the volumes.

Any two cubes are similar so the theorem applies.

The scale factor is 32/48 = 2/3 when simplified.

(2/3)³ = ratio of volumes of the smaller cube to the larger.

@not_so_smart

Answer 8

@not_so_smart yeah basically. The best way to convert on multiple choice is that.