Answer: Option B
Let us consider the given metal cube of edge 9 cm.
The volume of this cube will be given by the formula:
V1 = (Edge of cube)³= (9)³= 729 cubic cm
This cube is melted and formed into three smaller cubes. Let the edge of the third smaller cube be x cm. Therefore, the volume of each of the smaller cubes will be given by:
V2 = (Edge of first smaller cube)³= (1)³= 1 cubic cm
V3 = (Edge of second smaller cube)³= (6)³= 216 cubic cm
V4 = (Edge of third smaller cube)³= (x)³= x³ cubic cm
According to the law of conservation of mass, the volume of the smaller cubes must add up to the volume of the original cube. Hence, we have:
V2 + V3 + V4 = V1
1 + 216 + x³ = 729
x³ = 512
Taking the cube root on both sides, we get:
x = 8
Hence, the edge of the third smaller cube is 8 cm.
Therefore, the correct option is (B) 8 cm.
Summary:

• The original metal cube has an edge of 9 cm, and its volume is 729 cubic cm.
• It is melted and formed into three smaller cubes, with edges of 1 cm, 6 cm, and x cm.
• According to the law of conservation of mass, the volumes of the smaller cubes must add up to the volume of the original cube.
• Solving the equation 1 + 216 + x³ = 729, we get x = 8.
• Therefore, the edge of the third smaller cube is 8 cm, and the correct option is (B) 8 cm.