Pamela wants to buy a suitcase whose dimensions are 1 and 1/2 times those of her 28 X 16 X 8 in suitcase. How is the ratio of the volumes related to the ratio of the corresponding dimensions?

Question

directrix · Answer

If two solids are similar, the cube of the scale factor of the two solids is equal to the ratio of the volumes.

The volume of the smaller case is 28 X 16 X 8 = 3584 cubic inches.

So, we need the scale factor of the two suitcases.

That is from small to large case: 1 to (3/2) or 2 to 3.

So, 28 X 16 X 8 where V is the volume of the larger case.

directrix · Answer

The task is to solve this equation for V:

(2/3)^3 = 3584/V where V is the volume of the larger case.

directrix · Answer

@Girlsrule64  I just reread the problem. Are we to find the volume of the larger case or stop after saying that the ratio of the volumes is the cube of the ratio of corresponding dimension?

anonymous · Answer

how is the ratio of the volumes related to the ratio of corresponding dimensions?

directrix · Answer

Then, the ratio of the volumes is the cube of the ratio of the corresponding dimensions.