Two different positions of the same dice are shown, the six face of which are numbered from 1 to 6. Select the number that will be on the face opposite to the face having the number '3'.
1
In first and second dice 5, 6 are common in both dices.
First dice is rotated 90 0 anti-clockwise horizontally on the other adjacent side of 5, 6 is '1'.

∴ Here, the opposite face of side '3' is side '1'.
Hence, the correct answer is "1".
If 5 \(\sqrt{3}\) + \(\sqrt{75}\) = 17.32, then the value of 14 \(\sqrt{3}\) + \(\sqrt{108}\) is:
Two orientations of a dice are shown. This dice can be obtained by folding which of the option figures along the lines?

What is the cube root of 1728?