How many unit cubes would it take to construct the complete exterior of a hollow cube with edges of 4 units and faces 1 unit thick?
56
56
56
Yes, that is correct! The complete exterior of a hollow cube with edges of 4 units and faces 1 unit thick would require 56 unit cubes.
Well, constructing the complete exterior of a hollow cube with edges of 4 units and faces 1 unit thick is quite the puzzle. Let's break it down.
The hollow cube has an outer volume and an inner volume. The outer volume can be calculated by taking the total volume of the larger cube (4 * 4 * 4), minus the volume of the smaller cube (2 * 2 * 2). So, the outer volume is 64 - 8, which equals 56 cubic units.
Since each unit cube has a volume of 1 cubic unit, we can conclude that it would take 56 unit cubes to construct the complete exterior of the hollow cube.
Just imagine building a tower of 56 unit cubes with impressive engineering skills. That's quite a cube-tastic achievement!
To determine the number of unit cubes needed to construct the complete exterior of a hollow cube, we first need to find the volume of the solid cube and the volume of the hollow portion.
First, let's find the volume of the solid cube. The formula for the volume of a cube is given by V = s^3, where s represents the length of the side.
Given that the edges of the solid cube measure 4 units, the volume can be calculated as V = 4^3 = 64 cubic units.
Next, let's find the volume of the hollow portion. Since this is a cube with faces that are 1 unit thick, we need to subtract the volume of the inner cube from the volume of the solid cube.
The inner cube will have edges that are 2 units shorter on each side compared to the outer cube. So, the edge length of the inner cube would be 4 - 2 = 2 units.
The volume of the inner cube can be calculated as V = 2^3 = 8 cubic units.
To find the volume of the hollow portion, we subtract the volume of the inner cube from the volume of the solid cube: 64 - 8 = 56 cubic units.
Each unit cube represents a volume of 1 cubic unit. Therefore, the number of unit cubes required to construct the complete exterior of the hollow cube would be equal to the volume of the hollow portion, which is 56 cubic units.
Thus, it would take 56 unit cubes to construct the complete exterior of a hollow cube with edges of 4 units and faces 1 unit thick.