Math (geometry)
posted by Emily on .
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.

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!!

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 
Oh! I get it now. Thanks so much for helping!

Wnru