Question

A cube has edge length of 5. Another cube has edge length triple the original. Compute volume of new cube/ volume of original cube and reduce this ratio. Briefly describe the numerical relationship between the resulting ratio and the magnification factor of 3.

Answer 1

Ok, so what is the equation for the volume of a cube?

Answer 2

something cubed.

Answer 3

Side cubed. :)

So we have one cube with a side of 5. The other with a side of 3*5 (We could work this out, but for simplicity, we won't).

Thus, the volume of the cube with a side of 5 is: 5^3
And the volume of the cube with a side of 3*5 is: (3^3)*(5^3)

Answer 4

If we divide (3^3)*(5^3) by (5^3) we are left with 3^3, which is 9.

Answer 5

Okay. That makes sense. Is that all?

Answer 6

Well, you have to comment on the magnification factor of the side and it's relationship to the increase in volume. What would you say about it?

Answer 7

That's the part that I really needed help on. I'm not sure what to say.

Answer 8

A magnification of 3 leads to an increase in volume of 3^3, due to the volume being the edge cubed.

Also, 3^3 is not, in fact 9, heh. It's 27.

Answer 9

Yeah. I understand that. So my final answer should be along the lines of that?

Answer 10

Something like that, yeah. Use your own words. Anything you multiply the sides with will increase the volume by a factor that equals the cube of the factor (that you multiplied the side by)...if that makes sense

Answer 11

Oh, okay. Yeah. It makes sense.