Find the distance from one corner to another corner of a cube?

Question

how do u find the distance from one corner to the opposite corner of a cube if the edge of the cube is .281 nm?

Answer 1

You have to use Pythagoras' Theorem twice for this.

1) Find the distance from one corner to the opposite corner on the same face of the cube.  .281^2 +.281^2 = c^2

2) Now using c from step 1  we need to find the distance from one corner to the opposite (diagonal) corner  .281^2 + c^2 = d^2

3)  your answer is the value you get for d

Answer 2

Pythgaorean Theorem with a third dimension:

SQRT(.281^2 + .281^2 + .281^2) = .487

Answer 3

for a unit cube ..you go from (0,0,0) to (1,1,1)

this distance is ROOT(3)

for side =1 , diameter = root(3)

for side = .281, multiply by root(3) ...

.4867