The internal length, breadth and height of a cardboard box are 6 cm, 10 cm and 12 cm, respectively. How many boxes are needed in which cubes whose volume is 2160 cm³ can be packed?

The correct option is 3.

Step 1: Calculate the volume of one cardboard box
The formula for the volume of a rectangular box (cuboid) is given by:
$\text{Volume of a box}=\text{length}\times \text{breadth}\times \text{height}$

Given values:
Length ($l$) = 6 cm
Breadth ($b$) = 10 cm
Height ($h$) = 12 cm

$\text{Volume of 1 box}=6\text{cm}\times 10\text{cm}\times 12\text{cm}=720{\text{cm}}^3$

Step 2: Determine the number of boxes required
The volume of the cube to be packed is $2160{\text{cm}}^3$.

To find the total number of boxes needed to match/pack this volume, we divide the volume of the cube by the volume of one cardboard box:
$\text{Number of boxes}=\frac{\text{Volume of cube}}{\text{Volume of 1 box}}$

$\text{Number of boxes}=\frac{2160}{720}=3$

Thus, 3 cardboard boxes are needed.