Question

A cube has edges of length 3. If P and Q are points on its surface, what is the maximum straight-line distance from P to Q?

Answer 1

`3sqrt3` units, expanded to
`5.196`... units.

Explanation:

On your cube, the two points which are farthest apart would be opposite corners.

The method I used meant figuring the distance between two opposite corners which were still on the same face, and then using that distance in combination with the final distance in order to get the distance between two truly opposite corners.

First find the length of `bar A`, which you can use the Pythagorean theorem for:

`bar A=sqrt(3^2+3^2)`
`bar A=3sqrt2`

Now you can find the distance of `bar B` using the same method, but instead of two edges of the cube you can use `bar A` and `bar C` as your new legs:

`bar B=sqrt(bar A^2+3^2`
`bar B=sqrt(18+9)`
`bar B=sqrt(27)`
`bar B=3sqrt3`