The length, breadth and height of a box are in the ratio 3 : 2 : 1 respectively. The length of the box is 6 cm. Find the volume of the box.

1. Find the value of 1 unit in the ratio

Length is $3$ units.
$3\text{ units} = 6\text{ cm}$
$1\text{ unit} = 6 \div 3 = 2\text{ cm}$

2. Calculate the breadth and height of the box

Breadth $= 2\text{ units} = 2 \times 2 = 4\text{ cm}$
Height $= 1\text{ unit} = 2\text{ cm}$

3. Calculate the volume of the box

Volume $= \text{Length} \times \text{Breadth} \times \text{Height}$
Volume $= 6 \times 4 \times 2 = 48\text{ cm}^3$