Question

A diagonal of a cube goes from one of the cube's top corners to the opposite corner of the base of the cube, Find the length of a diagonal d in a cube that has an edge of length 10 meters. ​

Answer 1

d = 17.3 m

Explanation:

We can extend Pythagorean theorem to 3 dimensions by writing

`{d}^(2) = {x}^(2) + {y}^(2) + {z}^(2)`

or

`d = \sqrt{ {x}^(2) + {y}^(2) + {z}^(2) }`

Since we are dealing with a cube of side 10 m, then

x = y = z = 10 m

so we get

`d = \sqrt{ {10}^(2) + {10}^(2) + {10}^(2) }`

or

`d = \sqrt{3 * {10}^(2) } = 10 √(3) \: m`

This becomes

d = 17.3 m