Join 60,000+ competitive exam aspirants
A solid cube of side 6 cm is melted and recast into small cubes of side 2 cm. How many such small cubes can be formed?
8
16
24
27
27
When a solid object is melted and recast into smaller objects of the same material, the total volume remains conserved. By dividing the volume of the large cube by the volume of a single small cube, we find that exactly 27 small cubes can be formed.
When a solid object is melted and recast into smaller objects of the same material, the total volume remains conserved. By dividing the volume of the large cube by the volume of a single small cube, we find that exactly 27 small cubes can be formed.
Imagine melting a large block of chocolate to pour into smaller cubic molds; the total volume of chocolate stays constant, and the number of pieces depends on how many times smaller the new volume is.
V=s3 тАФ Volume of a cube where s is the side length
N=(ssmallтАЛslargeтАЛтАЛ)3 тАФ Number of recast similar solid objects
The principle of conservation of volume dictates that the total volume of matter remains constant during a geometric transformation or phase change, assuming no material is lost. The volume of any cube is given by the formula V=s3, where s is the side length. Therefore, the number of small cubes N is determined by the ratio of their volumes: N=ssmall3тАЛslarge3тАЛтАЛ=(26тАЛ)3=33=27.
Volume is conserved during melting and recasting processes.
Scaling factor for volume increases cubically with linear dimensions.
Metal casting and foundry operations in metallurgy
Injection molding in polymer manufacturing
Volume is measured in cubic units such as cm3.
Option A (8) incorrectly uses a linear ratio or miscalculates as 23, while Option C (24) is a common calculation trap.
D is correct тАФ 27 small cubes are formed because the ratio of the volume of the large cube to the small cube is 216/8=27.
Always verify whether a mensuration problem requires scaling of length (s), surface area (s2), or volume (s3).