Question 195238
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You might need to draw yourself a picture to verify this, but the diagonal of a cube forms the hypotenuse of a right triangle whose legs are one side of the cube and the diagonal of one of the faces of the cube.  So if a cube has a side length <b><i>s</i></b>, then the diagonal of a face is:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ d_f = \sqrt{s^2 + s^2} = s\sqrt{2}]


So then the diagonal of the cube is:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ d_c = \sqrt{s^2 + (s\sqrt{2})^2} = \sqrt{s^2 + 2s^2} = s\sqrt{3}]


So for your 10cm cube, the diagonal is


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ 10\sqrt{3}]


John
*[tex \LARGE e^{i\pi} + 1 = 0]
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