Question

two spheres of same metal weigh 1kg and 7kg. the radius of the smaller sphere is 3cm.the two spheres are melted to form a single big sphere. find the diameter of the new sphere(board 2015-foreign)

Answer 1

two spheres are of same metal therefore the density of both would be same.
density=mass/volume by using this expression u can calculate the volume the other sphere.(it will come out to be 7 times the smaller one)
Now you know the volume of both the spheres u can calculate the total volume and the volume will remain constant in the process of melting i.e.
V(net initial volume) = V(final volume)
and bam you will get the answer
the final radius will be 6 cm and thus the diameter will be 12 cm