2 answers

A diagonal of one cube is 2 cm

Question:

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!!

Answers

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!.

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