A solid cube of gold is melted and made into smaller cubes of sides half the original. How many such smaller cubes are made?

Solution

ATQ, When a solid cube is melted and then made into smaller cubes of sides half the original, each dimension of the original cube is halved. Let's denote the original side length as S. The volume of the original cube is S³ The new cubes have sides of length (S/2).The volume of each smaller cube is (S/3)³  This means that the original cube can be divided into 8 smaller cubes of sides half the original. Therefore, when a solid cube of gold is melted and made into smaller cubes of sides half the original, 8 such smaller cubes are made.