TNPSC Group II · Bite-size lessons
Area and Volume
About 6 min · Aptitude and Mental Ability · English
Time worked out from the lesson's 348 words at 150 words a minute, plus a minute for each question.
Area and Volume (Mensuration) is a listed topic in TNPSC Group II/IIA Aptitude section. Questions typically test your ability to calculate surface areas, volumes, and perimeters of standard 2D and 3D shapes.
Key ideas
- Area measures the surface covered by a 2D shape (in square units); Volume measures the space occupied by a 3D object (in cubic units).
- Perimeter/Circumference is the total boundary length of a 2D figure—often needed as an intermediate step.
- Lateral/Curved Surface Area (CSA) excludes the base(s); Total Surface Area (TSA) includes all surfaces.
- For 3D shapes, distinguish between hollow and solid objects—hollow objects have thickness affecting volume calculations.
- Unit consistency is critical: convert all measurements to the same unit before calculating. 1 m = 100 cm; 1 m³ = 1000 litres.
Watch out for
- Confusing radius and diameter → Always check whether the question gives radius or diameter. Halve the diameter before using formulas.
- Using height instead of slant height for cone CSA → Cone's curved surface needs slant height (l), not vertical height (h). Calculate l using Pythagoras.
- Forgetting to square or cube properly → Area involves r², volume involves r³. A small error in exponent creates large errors in answers.
Quick reference
- Equilateral triangle area: (√3/4)a² — memorize √3 ≈ 1.732
- Cylinder volume: πr²h — "Area of base × height"
- Cone volume: ⅓ × cylinder volume of same base and height
- Sphere volume: (4/3)πr³ — hemisphere is exactly half
- Always find slant height first for cone problems: l = √(h² + r²)
Check yourself: 3 questions
1. A rectangular water tank measures 8 m in length, 6 m in breadth and 3 m in height. How many litres of water can it hold when completely filled?
2. A circular park has a radius of 35 metres. What is the area of the park? (Use π = 22/7)
3. A cylindrical pillar has a diameter of 70 cm and height of 5 m. Find the curved surface area of the pillar. (Use π = 22/7)
This lesson is cut from the topic's note, not rewritten. Fact-checked on 17 Oct 2026: an AI-assisted check of this note against cited sources; the errors it found were corrected that day. Some errors may remain. The questions are from Shishya's validated question bank.
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