Question

The height, breadth and length of a cuboid are in the ratio 2:2:3. If the volume of the cuboid is 20736 cm3, find the length of the sides of the cuboid.

Answer 1

Answer :

Given : The height, breadth and length of a cuboid are in the ratio 2 : 2 : 3

Let ratio coefficient = x , So

Height of cuboid = 2x ,

Breadth of cuboid = 2x

And

Length of cuboid = 3x

We know volume of cuboid = Length $\times$ Breadth $\times$ Height
And given volume of cuboid = 20736 cm³
So,

3x $\times$ 2x $\times$ 2x = 20736

12x ³ = 20736

x ³ = 1728

x ³ = 12³

x = 12

So,

Length of cuboid = 3 ( 12 ) = 36 cm

Height of cuboid = 2 ( 12 ) = 24 cm

Breadth of cuboid = 2 ( 12 ) = 24 cm ( Ans )