UPSC Prelims 2002 Q20: Science & Technology – Quantitative Aptitude
Consider the volumes of the following:
1. A parallelepiped of length 5 cm, breadth 3 cm and height 4 cm
2. A cube of each side 4 cm
3. A cylinder of radius 3 cm and length 3 cm
4. A sphere of radius 3 cm
The volumes of these in the decreasing order is
- (a) I, III, II, IV
- (b) IV, II, III, I
- (c) I, II, III, IV
- (d) IV, III, II, I
Answer: (d) IV, III, II, I
Explanation
Volumes in decreasing order
| Solid | Volume (π ≈ 3.14) |
|---|---|
| 1. Parallelepiped 5 × 3 × 4 | 60 cm³ |
| 2. Cube of side 4 | 64 cm³ |
| 3. Cylinder r = 3, h = 3 | π × 9 × 3 = 84.8 cm³ |
| 4. Sphere r = 3 | (4/3) × π × 27 = 113.1 cm³ |
Arranged from the largest, the volumes are sphere (113.1), cylinder (84.8), cube (64) and parallelepiped (60). So the decreasing order is IV, III, II, I.
Answer: (d) IV, III, II, I.
Why each option is right or wrong
- (a) Incorrect. It puts the parallelepiped (60) first, though it is the smallest.
- (b) Incorrect. It puts the cube before the cylinder, but 64 < 84.8.
- (c) Incorrect. This is the increasing order of the numbering, not of volume.
- (d) CORRECT. 113.1 > 84.8 > 64 > 60.
Key point
Volumes: box lbh, cube a³, cylinder πr²h, sphere (4/3)πr³.
Remember
Sphere (113) > cylinder (85) > cube (64) > box (60).
Common mistakes
- Mixing the formulae of the sphere and the cylinder.
- Giving the cube a volume of 16 instead of 64.
- Ordering in increasing, not decreasing, order.
Exam tip
Compute only the two extremes first: sphere is largest, parallelepiped smallest.
Sources
- NCERT Class IX Mathematics — Surface Areas and Volumes
- Arun Sharma — How to Prepare for Quantitative Aptitude for the CAT (Geometry and Mensuration)