Question

a rectangular iron box has length 20 cm breadth 10 cm and height 5 cm. if it is melted and recast into cube. 8 such cubes make up a large block. what is the side of the larger cube

Answer 1

Maximum side of a cube $a = \textrm{5 cm}$    

Explantion:  

Given that,

Length of the iron box $l = \textrm{20 cm}$

height of the iron box $h = \textrm{5 cm}$

Breadth of the iron box $b = \textrm{10 cm}$

This box is divided into 8 cubes so the volume will always be constant,

As we know that, no of the cubes $\times$ Volume of a cube = Volume of iron box

⇒ $8\times a^{3} = l \times b \times h$    

⇒ $a^{3} = \frac{20 \times 10 \times 5}{8}$  

⇒ $a^{3} = 5^{3}$

Maximum side of a cube $a = \textrm{5 cm}$.