distance from one end to the other end of a cube?

Question

for example you had a cube you wanted to know the distance from one point to the oppsite side (longest length possible , or right thorugh the middle)
e.g. point a is (0,0,0) point b is (6,0,0) point c is (0,6,0) point d is (6,6,0) point e is (0,0,6) point f is (6,0,6) point g is (0,6,6) point h is (6,6,6)

so if i wanted the distance from a to h how would i get it, (0,0,0) to (6,6,6)

Answer 1

Distance between two points
= sqrt((x1-x2)^2 + (y1-y2)^2 + (z1-z2)^2)

sqrt((6-0)^2 + (6-0)^2 + (6-0)^2)
sqrt(6^2+6^2+6^2)
= 6sqrt(3)

Answer 2

Imagine cutting the block between the 2 points. You will get two identical pieces that are triangular prisms. The two sides of the prism that were unaffected have dimensions 6x6.

The new exposed face has dimensions of 6 x 6 √2
where 6 ² + 6 ² = length of the cut ²
length of the cut = 6 √2


So now you have a rectangle 6 x 6 √2 at one corner is (0,0,0) and the opposite corner is (6,6,6). Distance you want is "d"

d²=6² x (6 √2)²
d=6√3

Answer 3

You can find the distance between (0,0,0) and (6,6,6) by making different right triangles.

First, we know that a cube has equal lengthed sides.

We need to find the hypotenuse of the triangle formed from the points (0,0,0) to (6,0,0) and (6,6,0).

Use pythagora's equation to find the hypotenuse of this triangle which corresponds to the line going from (0,0,0) to (6,6,0).

The distance between (0,0,0) and (6,0,0) is 6.
The distance between (6,0,0) and (6,6,0) is 6.

a² +b ² = c²
6² + 6² = c²
72 = c²
c = 8,48 units

Therefore the distance between (0,0,0) and (6,6,0) is 8,48.

Then, knowing this, we form another triangle going from (0,0,0) to (6,6,0) to (6,6,6).

The distance between (0,0,0) and (6,6,0) is 8,48.
The distance between (6,6,0) and (6,6,6) is 6.

a² + b² = c²
8,48² + 6² = c²
72 + 36 = c²
108 = c²
c = 10.39 units.

We have discovered the distance between (0,0,0) and (6,6,6) is 10,39 units.

Answer 4

Do it in 2 steps. The first step would be to go from (a) to (d) and then from (d) to (h).
The first step gives you the diagional of a 6x6 square which is 6 sqrt(2). The second step involves finding the hypotenuse of a rt. triangle with sides of 6 and 6 sqrt(2), the hypotenuse being the cube diagional. The answer is sqrt(108), which can be simplified to 6 sqrt(3).

Answer 5

each side of the cube is 6 units.
In rectangle efgh, efh is a right angle triangle with fh as hypotenuse. Therefore,
fh^2=ef^2+eh^2
=6^2+6^2
=72

The distance from a to h, is hypotenuse of right angle triangle afh, therefore,
ah^2=af^2+fh^2
=6^2+72 (as calculated above)
=36+72=108
ah=√108=6√3=10.39

Answer 6

ANS: 1.732 times the side of Cuibe.

Let the Side of CUBE be x.

then Normal Side Diagonal = Root2 times x

Thus Solid Diagonal = Sq. root ( x^2 + 2x^2)

= 1.732 times x.

Answer 7

a,b,c,d = 6x6x6x6
e,f,g,h = 6x6x6x6
First solve f to h. square root of 72
a to f = 6 or the square root of 6squared
so a to h would be the square root of 6squared + the square root of 72. Square root of 108 is distance from a to h
Approx. 10.3