Metallic spheres of radii , and respectively are melted to form a single solid sphere. Find the radius of the resulting sphere.
Step 1. Determine the volumes of the given three spheres.
Let the radii of the given spheres be , and respectively.
Given: , and .
Now, Volume of a sphere
The volume of the first sphere:
The volume of the second sphere:
The volume of the third sphere:
Step 2: Find the radius of the resulting sphere.
Let be the radius of the resulting sphere.
As the three spheres are melted to form a single new sphere.
Therefore,
Hence,
Hence, the radius of the resulting sphere is .