The length of an edge of a hollow cube open at one face is $\sqrt{3}$ metres. What is the length of the largest pole that it can accommodate?

### Concept & Formula The length of the largest pole that can be accommodated in a cube (whether hollow, open at one face, or closed) is equal to its main body diagonal. The opening on one face does not change the internal maximum distance from one corner to the opposite corner. $$Diagonal = a\sqrt{3}$$ Where $a$ is the length of the edge. ### Step-by-Step Solution 1. **Given:** The edge length of the cube, $a = \sqrt{3}$ metres. 2. **Calculation:** Substitute the value of $a$ into the body diagonal formula. 3. $Diagonal = (\sqrt{3}) \times \sqrt{3}$ 4. $Diagonal = 3$ metres. ### Exam Strategy & Shortcut Don't let the phrase "hollow cube open at one face" trick you into calculating something different like a face diagonal or subtracting anything. The longest internal distance in any rectangular prism or cube is always the main diagonal. Simply multiply the side by $\sqrt{3}$. ### Common Pitfall A common mistake is thinking the "open face" means you can only place a pole along the open surface or confusing the body diagonal with the face diagonal ($a\sqrt{2}$). ### Final Answer Therefore, the correct answer is **3 m**.