Question

How many 34-centimeter cubes do you need to create a cube with an edge length of 12 centimeters?

Answer 1

since 12 is less than 34, and does not divide 34, I suspect a typo.

If you meant 3/4 cm cubes, then
since 12 = 3/4 * 16, you would need 16^3 = 4096 small cubes to make the large one.

Answer 2

The volume of a cube is the length cubed: V = l3. If the length is 12, the volume is 123=1728 cm3.

I can't tell if the 3/4 is the length of the cube or the volume, but I will start by assuming it's the volume (meaning the cubes have a volume of 3/4 cm3 each). To find how many of these cubes are needed to make the larger cube, just divide the larger by the smaller: 1728/(3/4) = 2308. 2308 cubes are needed.

If 3/4 is the length, each 3/4 cm cube has a volume of (3/4)3 = 27/64 cm3. This changes the final calculation to: 1728/(27/64) = 4096. 4096 cubes are needed in this case.

The distinction is tricky but important: a cube with 3/4 cm length is not the same as a cube of 3/4 cm3 volume.