How do you calculate the distance of a cube from the center to the corner?

Answer 1

Looking for a quick answer? It's...

x√(3)

2

Looking for an explanation, too? It's below.

If the cube's sides are length x, and if we create a right triangle using two of the edges, then a diagonal of one of the faces, by the Pythagorean Theorem, is x√(2).

a2+b2=c2

x2+x2=c2

2x2=c2

√(2x2)=√(c2)

c = √(2x2)

c = x√(2)

So if the diagonal of a face of a cube is x√(2), and if we create a triangle with the sides of that diagonal, any side not on its face, and the diagonal in the middle of the cube connecting them, we can use the Pythagorean Theorem again.

a2+b2=c2

(x√(2))2+x2=c2

2x2+x2=c2

√(3x2)=√(c2)

c = √(3x2)

c = x√(3)

That is the length of a diagonal of the cube. Since the center is halfway through that diagonal and a corner is at the end, simply dividing by 2 will do the trick.

x√(3)

2

Just replace x with whatever the length of the side is, and you have your distance from a vertex to the center.