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.

---------------------------------------------------------------------------------------------------

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

## Answer this Question

## Related Questions

- Math - damn i cant post a drawing..there r 2 cubes, cube x and cube y and the ...
- Science - Sarah heated two cubes of aluminum to 50 degrees celsius. Cube B has a...
- algebra - the cube root of the volume of a cube gives the length of one side of ...
- Algebra 1 - The cube root of the volume of a cube gives the length of one side ...
- College Algebra - The ratio of the surface area of a solid cube to its volume is...
- pre-calculus - Express the edge length of a cube as a function of the cube's ...
- Geometry - A sphere is inscribed in a cube. The diagonal of one face of the cube...
- Science - Michael dropped a 1 inch cube of wood and a 1 inch cube of laed into ...
- MATH! - If the edge of a cube is increased by 50%, then the volume is increased ...
- Math - * Which is performing more efficiently? A car getting 12 km per liter of ...