The length, breadth and height of a cuboid are in the ratio of 3 : 4 : 5 and its volume is 3840 cm³. The smallest side has a length of?

12 cm

Let the length, breadth, and height of the cuboid be:

$3x,\ 4x,\ 5x$

The volume of a cuboid is:

$\text{Volume} = l \times b \times h$

So,

$3x \times 4x \times 5x = 3840$

$60x^3 = 3840$

$x^3 = \frac{3840}{60} = 64$

$x = 4$

Hence the dimensions are:

• Length = $3x = 12\text{ cm}$
• Breadth = $4x = 16\text{ cm}$
• Height = $5x = 20\text{ cm}$

The smallest side is 12 cm.