# Which is the longest stick that can be contained inside a cube with side length 1 m? Please show calculation! What you are searching is the longest line inside the cube which is of course space diagonal.

Formula for the length of space diagonal of a cuboid is

`d=sqrt(a^2+b^2+c^2)`

where `a,` `b` and `c` are lengths of the edges. Since cube has all equal sides formula for space diagonal of a cube is

...

## See This Answer Now

Start your 48-hour free trial to unlock this answer and thousands more. Enjoy eNotes ad-free and cancel anytime.

What you are searching is the longest line inside the cube which is of course space diagonal.

Formula for the length of space diagonal of a cuboid is

`d=sqrt(a^2+b^2+c^2)`

where `a,` `b` and `c` are lengths of the edges. Since cube has all equal sides formula for space diagonal of a cube is

`d=sqrt(a^2+a^2+a^2)=sqrt(3a^2)=asqrt3`

Hence if `a=1"m"` then

`d=1sqrt3=sqrt3approx1.732`  ` `

The length of the longest stick that can be containdes in cube with side length of 1m is `sqrt3"m."`

Approved by eNotes Editorial Team