Answer:
The number cubes needed when we have three cubes along each edge is 27 cubes
Step-by-step explanation:
The given parameters for the building of a cubic prism are;
The number of cubes used to build the 2 by 2 cube = 8 cubes
Let 'x' represent the length of each cube, we have;
The volume of a 2 by 2 cube = 2·x × 2·x × 2·x = 8·x³
Where x³ represents the volume of each cube
When we have three cubes along each edge, the total volume, becomes;
V = 3·x × 3·x × 3·x = 27·x³
The number cubes needed when we have three cubes along each edge, n = (The total volume of the cubes)/(The volume of each cube)
∴ The number cubes needed when we have three cubes along each edge, n = 27·x³/(x³/cube) = 27 cubes.
