The length, breadth and height of cuboid are in the ratio 3 : 2 : 1 and its volume is 162 cm³; the longest side of the cuboid is:

1. 6 cm

2. 9 cm

3. 18 cm

4. 54 cm

Given:

The length, breadth and height of cuboid are in the ratio 3 : 2 : 1.

The volume of the cuboid = 162 cm³.

Let the length, breadth and height of cuboid be 3a, 2a and a, respectively.

As we know that volume of cuboid = length x breadth x height

⇒ 3a x 2a x a = 162 cm³

⇒ 6a³ = 162

⇒ a³ = $\dfrac{162}{6}$

⇒ a³ = 27

⇒ a = $\sqrt[3]{27}$

⇒ a = 3 cm

Largest length of the cuboid = 3a

= 3 x 3 cm

= 9 cm

Hence, option 2 is the correct option.