Mensuration
About 6 min · Numerical Ability · English
Time worked out from the lesson's 409 words at 150 words a minute, plus a minute for each question.
Mensuration deals with the measurement of geometric shapes — calculating perimeter, area, surface area, and volume. The questions typically involve basic 2D shapes (rectangles, circles, triangles) and simple 3D solids (cubes, cylinders, cuboids).
Key ideas
- Perimeter is the total boundary length of a 2D shape; Area is the space enclosed within that boundary.
- Surface Area of a 3D solid is the total area of all its faces; Volume is the space it occupies.
- For 3D solids, distinguish between Curved Surface Area (CSA) — only the curved portion — and Total Surface Area (TSA) — curved plus flat faces.
- When a shape is inscribed in another (e.g., circle in square), their dimensions share a relationship — identify the connecting element (diagonal, diameter, side).
- Units matter: Area uses square units (cm², m²), Volume uses cubic units (cm³, m³). Converting between units requires squaring or cubing the conversion factor.
Watch out for
- Confusing radius and diameter → Always check what's given. Diameter = 2 × radius. Halve the diameter to get the radius when diameter is provided before applying formulas.
- Mixing up CSA and TSA → Read carefully whether the question asks for "curved surface" or "total surface." A closed cylinder's TSA includes two circular ends; CSA does not.
- Forgetting to square/cube when converting units → 1 m² = 10,000 cm² (not 100). 1 m³ = 1,000,000 cm³. Always square for area, cube for volume.
Quick reference
- Square: Area = side², Diagonal = side × √2
- Circle: Area = πr², Circumference = 2πr
- Cylinder volume = πr²h; Cube volume = a³
- Sphere volume = (4/3)πr³; Hemisphere volume = (2/3)πr³
- TSA of cylinder = 2πr(r + h); CSA of cylinder = 2πrh
Check yourself: 3 questions
1. The length of a rectangle is 24 cm and its breadth is 18 cm. If the length is increased by 25% and the breadth is decreased by 20%, what will be the percentage change in the area of the rectangle?
2. A circular park has a circumference of 440 metres. A path of uniform width of 7 metres runs around the outside of the park. What is the area of the path in square metres?
3. The area of a square is equal to the area of a circle. If the perimeter of the square is 88 cm, what is the circumference of the circle? (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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