UPSC Prelims 2002 Q64: Science & Technology – Quantitative Aptitude
The length of the longest pole that can be placed in a room 12 m long and 9 m wide and 8 m
high is
- (a) 12 m
- (b) 14 m
- (c) 17 m
- (d) 21 m
Answer: (c) 17 m
Explanation
Longest pole in a room of given length, width and height
| Item | Value |
|---|---|
| Length × width × height | 12 m × 9 m × 8 m |
| Longest pole | The space diagonal of the room |
| Formula | √(l² + b² + h²) |
| Calculation | √(144 + 81 + 64) = √289 = 17 m |
The longest pole that can be placed in a room is its space diagonal. For a room 12 m long, 9 m wide and 8 m high it is √(12² + 9² + 8²) = √289 = 17 m.
Answer: (c) 17 m.
Why each option is right or wrong
- (a) Incorrect. 12 m is only the length of the room.
- (b) Incorrect. 14 m is smaller than the space diagonal of 17 m.
- (c) CORRECT. √289 = 17 m is the space diagonal.
- (d) Incorrect. 21 m is the sum 12 + 9, not the diagonal.
Key point
Space diagonal of a cuboid = √(l² + b² + h²); the 8-15-17 and 9-12-15 triples help.
Remember
Longest pole = √(l² + b² + h²).
Common mistakes
- Adding the three sides (29 m) rather than using the root.
- Using only the floor diagonal √(144 + 81) = 15 m.
- Forgetting the height term in the root, which gives 15 m.
Exam tip
144 + 81 + 64 = 289 = 17², a perfect square, so the answer is clean.
Sources
- NCERT Class IX Mathematics — Surface Areas and Volumes
- Arun Sharma — How to Prepare for Quantitative Aptitude for the CAT (Geometry and Mensuration)