Question

A cuboid has dimension of $6\text{m}\times 4\text{m}\times 8\text{m}.$ The cuboid is broken into maximum number of cubes such that no part of cuboid is left. Find the perimeter of one such cube.

• A. $12\text{m}$
• B. $8\text{m}$
• C. $6\text{m}$

Answer 1

The correct option is A $12\text{m}$

Dimension of cuboid $=\text{length}\times \text{breadth}\times \text{height}$
$=6\text{m}\times 4\text{m}\times 8\text{m}$

Cube has sides of equal dimension.

The dimension of the largest cube is the greatest common factor of the length, breadth and height of the cuboid.

Factor Trees of $6,4$ and $8$ are:

$\to 6=2\times 3$
$\to 4=2\times 2$
$\to 8=2\times 2\times 2$

The common factor of all the three numbers is $2.$
$\therefore$ The largest possible cube must have side length of $2\text{m}.$
Perimeter of one cube $=6\times \text{side}=6\times 2=12\text{m}$