Mensuration
About 6 min · Quantitative Aptitude (Basic Arithmetic Skill) · English
Time worked out from the lesson's 315 words at 150 words a minute, plus a minute for each question.
Mensuration is the mathematical study of measurement — specifically the area, perimeter, surface area and volume of geometric figures.
Key ideas
- Perimeter vs Area: Perimeter is the boundary length (measured in units like cm, m); area is the space inside (measured in square units like cm², m²). Never mix units.
- Surface Area vs Volume: For 3-D objects, surface area is the total outer covering (square units); volume is the space occupied (cubic units like cm³, m³).
- Radius–Diameter Relationship: Diameter = 2 × Radius. In circle formulas, always check whether the given value is r or d.
- π Approximation: Use π = 22/7 or 3.14 depending on the question. If the question has 7, 14, 21 as lengths (multiples of 7), use 22/7; otherwise use 3.14.
- Composite Figures: Many problems combine shapes (e.g. a rectangle with a semicircle on top). Break them into standard shapes, calculate separately, then add/subtract as needed.
Quick reference
- Circle area–circumference link: If circumference = 2πr, then area = πr² — both depend on radius.
- Cube diagonal (space diagonal): a√3 where a is the edge.
- Cylinder to cone volume ratio: For same base and height, cylinder volume = 3 × cone volume.
- Sphere to hemisphere volume: Sphere = 2 × hemisphere (same radius).
- Melting/Recasting: Volume before = volume after; shape changes, volume doesn't.
Check yourself: 3 questions
1. The area of a square field is 1600 square metres. Find the cost of fencing it at the rate of Rs. 5 per metre.
2. A cone and a cylinder have equal bases and equal heights. If the volume of the cylinder is 150 cubic cm, what is the volume of the cone?
3. A cylindrical tank has a radius of 7 cm and a height of 10 cm. What is its volume? (Use π = 22/7)
This lesson is cut from the topic's note, not rewritten. Fact-checked on 18 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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