Finding Out the Diagonal of Cube and Cuboid

Calculate the length of face diagonal of the cube whose side is $12\sqrt{3} \mathrm{cm}$ long. What is the length of the space diagonal of that cube?

Calculate the length of the possible longest pole in meter, which can be placed in a room of length $10 \mathrm{m}$, width $10 \mathrm{m}$ and height $5 \mathrm{m}$.

A cuboid is of length $8 \mathrm{m}$, breadth $4 \mathrm{m}$ and height $2 \mathrm{m}$. Calculate the lengths of all the diagonals.