## volume of HCP unit cell from radius + c/a ratio

1. The problem statement, all variables and given/known data
Cobalt has an HCP (hexagonal close packed) crystal structure, an atomic radius of 0.1253 nm and a c/a ratio of 1.623. Compute the volume of the unit cell for cobalt.

2. Relevant equations
area of hexagon = apothem*perimeter/2

3. The attempt at a solution
calculate 1 of the 6 sides (2 atomic radii per side):
2*.1253 = 2.506e-1

calculate perimeter:
2.506e-1*6 = 1.5036e+0

calculate height:
2.506e-1*1.623 = 4.06724e-1

calculate hexagon area (apothem = 2 radii):
1.5036e+0*2.506e-1 / 2 = 1.88401e-1

calculate volume:
1.88401e-1*4.06724e-1 = 7.66272e-2