A rectangular prism has a length of 4", a width of 8", and a height of 12". If both the length and height double, how many times larger is the new volume than the original volume?

Question

A rectangular prism has a length of 4", a width of 8", and a height of 12".  If both the length and height double, how many times larger is the new volume than the original volume?

anonymous · Answer

I will give medals for an answer with all of the steps and will fan dont have enpough time to learn how to do it have to turn it in:(

whpalmer4 · Answer

Volume of a rectangular prism is $$V = l*w*h$$

If you make the prism twice as long, by substituting $2l$ in place of $l$, what happens to the volume?  If you then make the prism twice as tall by substituting $2h$ in place of $h$, what happens to the volume?

anonymous · Answer

I dont know, but its do,, could you please please Give me the answers?

whpalmer4 · Answer

I could, but that's not how I roll.  I'd rather you know how to do it, and knowing how to do it is simple.

Volume of the original box is $$V=l*w*h$$if we double the length, by putting in $2l$ instead of $l$, we'll have a new volume of $$V_{new} = (2l)*w*h = 2 * l * w *h$$Doesn't matter what any of the dimensions are: if we double one of them, the volume doubles.

This should be pretty obvious if you think about it.  Doubling one of the dimensions is exactly equivalent to having one block with the original dimensions, and adding another block with the original dimensions.  Presto, change-o, you've got twice the volume.

Now, if we do that in two dimensions, what happens to our volume?