Question

2 sphere of same metal weight 1 kg and 7 kg.The radius of the smaller sphere is 3 cm. The two sphere are melted to form a single big sphere ,find the diameter of the new sphere

Answer 1

Answer:

12 cm

Step-by-step explanation:

As these are made from the same metal, the sphere that has 7 times more weight than the other, has 7 times more volume than the other.

The volume of the smaller sphere is

(4/3) π 3³

so the volume of the larger sphere is

7 × (4/3) π 3³.

Combining the metal from both, the total volume of metal that we have is

(4/3) π 3³  +  7 × (4/3) π 3³  =  8 × (4/3) π 3³.

Let r be the radius of the single big sphere that we make in the end.  As its volume is the volume of all the metal, we have

Volume of single big sphere = (4/3) π r³ = 8 × (4/3) π 3³

=> r³ = 8 × 3³ = 2³ × 3³

=> r = 2 × 3 = 6.

The diameter is twice the radius and so is 12 cm.