How many 34-centimeter cubes do you need to create a cube with an edge length of 12 centimeters?
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.
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.
To find the answer, we need to calculate the volume of both the small cubes and the larger cube.
The volume of a cube is calculated by multiplying the length of one side by itself twice. So, for a 34-centimeter cube, the volume would be (34 cm) * (34 cm) * (34 cm) = 39304 cubic centimeters.
Now, let's calculate the volume of the larger cube with an edge length of 12 centimeters. The volume of this cube can be found using the same formula: (12 cm) * (12 cm) * (12 cm) = 1728 cubic centimeters.
To find out how many 34-centimeter cubes are needed to create the larger cube, we need to divide the volume of the larger cube by the volume of the smaller cube. So, 1728 cubic centimeters / 39304 cubic centimeters = 0.044, approximately.
This means that only a fraction of a 34-centimeter cube is needed, so it is not possible to create the larger cube using only 34-centimeter cubes.