Question

Can someone find the expression for h in terms of x.

Answer 1

The volume of the cylinder is equal to the sum of all spheres
the volume of 1 sphere is V1=4/3×pi×(1/2 x)³
simplified V1=1/6×pi×x² 
we conclude that the volume of the cylinder is V2=270V1
V2=45×pi×x³
also the V2 can be calculated from the cylinder 
V2= base(circle)×height
V2=(3x)²×pi×h=9x²×h
so we have 
9x²×pi×h=45×pi×x³
simplified h=5x