A solid metallic cuboid of sides 4 cm × 10 cm × 15 cm is melted and made into small identical dices of 2 cm × 2 cm × 2 cm. How many such dices can be made? 

Correct option is A

Given:

Sides of cuboid  = 4 cm × 10 cm × 15 cm

Sides of dices = 2 cm × 2 cm × 2 cm

Formula Used:

​$$Volume of cuboid=length×breadth×height$$​​

Solution:

A solid metallic cuboid is melted and made into small identical dices so: 

Dimensions of the cuboid are given as 4 cm × 10 cm × 15 cm so:  

Volume of cuboid = 4cm × 10cm × 15cm = 600 $$cm^3$$ 

Dice has dimensions 2 cm × 2 cm × 2 cm so:

Volume of one dice = 2cm × 2cm × 2cm = 8 $$cm^3$$ 

​$$\text{Number of dices} = \frac{V_{\text{cuboid}}}{V_{\text{dice}}} = \frac{600 \, \text{cm}^3}{8 \, \text{cm}^3} = 75 \\$$ 

​Thus the number of small dices that can be made is 75.