Question 1
A tank measures 2 m × 4 m × 5 m.
What is its volume?
- 44
- 76
- 11
- 8
- 40
Show the worked solution
- Volume = length × breadth × height = 2 × 4 × 5 = 40 m³.
- Answer: 40 m³.
Mensuration
Mensuration questions — the formulas, and when each one applies
Mensuration questions ask for the area, perimeter, surface area or volume of a standard shape. The marks are lost to two things and not to the formulas: mixing units within one question, and reading total surface area as curved surface area. Fix the units first, then confirm which surface the question actually wants.
Mensuration is worth two to four marks in most bank and SSC papers and is entirely recall plus care. Nothing in it requires insight, which cuts both ways: a candidate who knows the formulas and reads carefully gets full marks quickly, and one who half-remembers loses marks on questions they genuinely understood.
Try it against the clock. Mensuration runs at 35s easy, 45s medium and 60s hard. The clock is stamped and judged on our server, so the limit you see is the deadline that is actually enforced — and it starts when you tap Start, not while the question is loading.
How to solve mensuration questions without a unit slip
-
Convert every measurement to one unit before starting
A question mixing metres and centimetres is not testing your formula, it is testing whether you noticed. Convert everything as you read, and write the unit beside each number rather than trusting yourself to remember it.
-
Decide which surface the question wants
Curved surface area excludes the ends; total surface area includes them. For a cylinder that is 2πrh against 2πr(r + h). Both appear in the option list of a well-set question, so read the phrase before reaching for a formula.
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Keep π symbolic until the last step
Carry π through the working and substitute 22/7 only at the end, and only if the question's numbers make it cancel. Most exam questions choose radii that are multiples of 7 precisely so it does — substituting early creates decimals that never needed to exist.
-
Use ratio reasoning when a dimension changes
If a radius doubles, area scales by four and volume by eight — no recomputation is needed. A large share of mensuration questions ask exactly this, and answering by scaling is a few seconds against a minute.
The formulas worth having instantly
| Shape | Formula |
|---|---|
| Circle | Area πr², circumference 2πr |
| Cylinder | Volume πr²h · CSA 2πrh · TSA 2πr(r + h) |
| Cone | Volume ⅓πr²h · CSA πrl · slant l = √(r² + h²) |
| Sphere | Volume ⁴⁄₃πr³ · surface 4πr² |
| Cuboid | Volume lbh · TSA 2(lb + bh + hl) |
| Scaling a linear dimension by k | Area × k², volume × k³ |
3 real mensuration questions, with worked solutions
Generated by the same engine that mints the ComputePrep daily. Each answer is computed from the numbers printed in the question, and the walkthrough below each one is the engine's own working — not a solution written afterwards. Reload this page's live drill and you get different numbers.
Question 2
A square plot has a side of 19 m.
What is its perimeter?
- 38
- 76
- 46
- 361
- 90
Show the worked solution
- Perimeter = 4 × side = 4 × 19 = 76 m — perimeter is a length, area is a square.
- Answer: 76 m.
Question 3
A circular park has a radius of 7 m. (Take π = 22/7.)
What is its area?
- 308
- 44
- 154
- 164
- 49
Show the worked solution
- Area = πr² = (22/7) × 7 × 7 = 154 m².
- Answer: 154 m².
Common mistakes this drill is built from
The wrong options are not random numbers. Each one is the result of a specific careless error for this topic, so picking one tells you which habit is costing you marks.
Mixing units inside one question
Metres with centimetres, or litres with cubic centimetres. Convert at the point of reading, not at the point of computing, and the error becomes impossible rather than merely unlikely.
Using the height where the slant height is required
A cone's curved surface uses the slant l, not the vertical height h. Where only h and r are given, l = √(r² + h²) comes first. The answer using h is always among the options.
Recomputing instead of scaling
When a question doubles or halves a dimension, the answer follows from k² or k³ directly. Rebuilding the whole calculation is slower and introduces arithmetic that was never needed.
Why your answer came out wrong
The specific wrong numbers this topic produces, and what each one tells you about the step you took. If you have just got a question wrong and want to know which habit did it, start here.
The radius is in centimetres and the height in metres — do I really have to convert?
Always, and before you substitute, not after. A stray metre among centimetres inside a formula that cubes the length puts the answer out by a factor of a million, and inside an area formula by ten thousand. Convert both to one unit on the first line of your working.
When does a cone question need the slant height rather than the height?
Curved and total surface area use the slant height l; volume uses the vertical height h; and l² = h² + r² connects them. Substituting h where l belongs gives a smaller, entirely plausible answer that the paper prints. If the question asked for a surface area and you never used Pythagoras, check which one you used.
The radius doubles — should I recompute the volume from scratch?
No, scale it. Volume grows with the cube of the radius, so it multiplies by 8; surface area grows with the square, so by 4. Recomputing with π and fractions takes the best part of a minute, and scaling takes five seconds.
FAQ
What is the difference between curved and total surface area?
Curved surface area covers only the curved part — for a cylinder, 2πrh. Total surface area adds the flat ends, giving 2πr(r + h). Questions ask for both and the option list carries both values, so the deciding step is reading which one is wanted, not knowing the formula.
When should I use 22/7 for π?
Only at the final step, and only when the radius is a multiple of 7 so it cancels cleanly. Exam questions almost always choose radii for exactly that reason. Substituting early turns an exact calculation into an awkward decimal for no benefit.
If the radius of a sphere doubles, what happens to its volume?
It multiplies by eight. Volume scales with the cube of any linear dimension, and surface area with the square, so doubling the radius gives 2³ = 8 times the volume and 2² = 4 times the surface area. Recognising this answers a whole family of questions without recomputation.
Practise the next topic
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- Vedic maths shortcuts — the seven sutras that make a 15-second answer possible.
- How to improve calculation speed — the six-week arc these drills fit into.
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