for face centered unit cell, r=6

Question

find edge in terms of r, face diagonal in terms of r, body diagonal in terms of r,

edge=squareroot(8)r
face=4r
but i don't know how to find body diagonal

Answer 1

Isn't the face diagonal
4r = a*2^1/2
The body diagonal is a*3^1/2 .

The triangle has sides of a (the upright line on the left side of the unit cell), the diagonal (along the floor of the unit cell which we know is a*2^1/2 so the body diagonal is the hypotenuse of that triangle. So d_b² = a² + (a*2^1/2)²
I hope this turns out right.

Answer 2

It looks ok to me. You solve, of course, for d_b² then take the square root of it. That should be the d_b = a*3^1/2

Answer 3

for body diagonal. take face diagonal and square it and take edge diagonal and square it. add those 2 together than take the SQUARE ROOT of it. Answer. so its basically the a^2+b^2=c^2 equation.