Posted by **Emily** on Thursday, April 3, 2008 at 11:26pm.

A diagonal of one cube is 2 cm. A diagonal of another cube is 4*sqrt3 cm. The larger cube has volume 64 cubic cm. Find the volume of the smaller cube.

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There was this theorem mentioned in the lesson where if the scale factor of two similar solids is a to b, then

1) the ratio of corresponding perimeters is a to b.

2)the ratio of the base areas, of the lateral areas, and of the total areas is a squared to b squared.

3) the ratio of the volumes is a cubed to b cubed.

Does anybody know how to do this? Thanks for all of your help!!

- Math (geometry) -
**drwls**, Friday, April 4, 2008 at 12:12am
The theorem you mentioned is true but I won't try to prove it here. In your case, since a linear dimension of the cube increases by a factor of 2 sqrt 3 compared to the smaller cube, The larger cube has a volume that is (2 sqrt3)^3 larger.

That equals 2^3 * 3^(3/2)= 41.57 times

(or 24*sqrt3) larger in volume

- Math (geometry) -
**Anonymous**, Wednesday, March 6, 2013 at 11:17pm
Wnru

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