solid state

THE Packing will be formed with triangular voids..

So there is an equilateral triangle kind of a void (ofcourse curved..)

now the area of the circular part (covered by the cylinder) will be Ï€r²/2

while the correspoinding triangle will have an area of √3/4 * (2r)^2

Now the ratio will be Ï€2√3=.90...

Cehck for calculations