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Which is the longest stick that can be contained inside a cube with side length 1 m?...

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Jackly | eNotes Newbie

Posted November 5, 2013 at 9:05 PM via web

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Which is the longest stick that can be contained inside a cube with side length 1 m?

Please show calculation!

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tiburtius | High School Teacher | (Level 3) Associate Educator

Posted November 5, 2013 at 9:27 PM (Answer #1)

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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."`

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