Calculating c/a ratio for h.c.p

[mate1000]

iv been asked to show that the ideal c/a ratio for a hexagonal close packing unit cell is 1.633. The only thing i could come up with was to do with the atomic packing factor. where i get (4/3pi^2r*6) / (3a*2r*c). Am i heading in the right direction or am i way off course. If I am way off would anyone be able to give me a hand?
Cheers

 

[Gokul43201]

The packing factor isn't useful. This is simply a question of 3d geometry. Draw a picture of the HCP unit cell with spherical atoms and start there.

Hint: What do you know about the position of the centroid of an equilateral triangle?