Question

There are 38 Cube Houses. Each house could hold 1,000 unit cubes that are 1 meter by 1 meter by 1 meter. Describe the dimensions of a cube house using unit cubes. Remember that the edges of a cube are all the same length. PLEASE HELP!

Answer 1

So each house can hold 1000 cubes that are 1 meter in length. The house is also shaped like a cube, so you need to cube-root 1000. The cube-root of 1000 is 10. So the cube house has a length, width, and height of 10 meters.

Answer 2

The problem is giving us the total volume of each house (1000 unit cubes), and is asking us for the dimensions of the cube house.

We can solve this using the volume equation for the cube:

$Volume_{cube} =Side_{cube} ^{3}$

we solve for side (edge) which is what we look for

$Side_{cube}=\sqrt[3]{Volume_{cube} }$

$Side_{cube}=\sqrt[3]{1000 unit cubes }\\Side_{cube}=10 unit cubes$

like it is said in the problem the cube has the same dimensions for all three edges so the house would be 10 unit cubes high, 10 unit cubes deep and 10 unit cubes long