Mensuration
About 6 min · Mathematics · English
Time worked out from the lesson's 383 words at 150 words a minute, plus a minute for each question.
Mensuration is the quantitative study of geometric figures — computing area, perimeter, surface area and volume. Questions test both formula recall and the ability to apply formulas to word problems involving real-world objects like water tanks, metal sheets, ground plots, and packaging.
Key ideas
- Area measures the space inside a 2-D boundary; units are always square (cm², m², etc.). Perimeter measures the boundary length itself.
- Surface area for 3-D solids comes in two flavors: lateral (curved) surface area excludes the top/bottom bases; total surface area includes all faces.
- Volume measures the space a 3-D object occupies; units are cubic (cm³, m³). One cubic metre = 1000 litres; one litre = 1000 cm³.
- The number π (pi) appears in all circular formulas. Use π = 22/7 or 3.14 as instructed.
- For composite figures, break them into standard shapes, compute each separately, then add or subtract areas/volumes as needed.
Watch out for
- Confusing radius and diameter → Always confirm whether the problem gives r or d. If diameter = 14, radius = 7. Many students plug d directly into r formulas and get a 4× error.
- Using lateral SA when total SA is asked → Read carefully: "curved surface area" excludes bases; "total surface area" includes them. For painting a closed tank, use TSA; for a tube open at both ends, use CSA only.
- Forgetting unit conversions → Mixing metres and centimetres inflates or deflates answers by factors of 100 or 1000. Convert everything to one unit before computing.
Quick reference
- Square diagonal: side√2
- Cube space diagonal: side√3
- Cylinder: Volume = πr²h; Curved SA = 2πrh
- Cone: Volume = (1/3)πr²h; slant height l = √(r² + h²)
- Sphere: Volume = (4/3)πr³; Surface Area = 4πr²
Check yourself: 3 questions
1. A rectangular plot of land measures 25 m in length and 18 m in breadth. What is the area of the plot in square metres?
2. The total surface area of a cube is 384 sq cm. What is the length of one edge of the cube?
3. A cone has a base radius of 6 cm and a slant height of 10 cm. What is the curved surface area of the cone? (Use π = 3.14)
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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