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The Chapter You Cannot Afford to Guess
Mensuration is the one arithmetic chapter where the question is never hard and the marks are still lost. Nobody fails to find the volume of a cylinder because the idea is difficult; they fail because they wrote 2πrh when the paper asked for the total surface area, or because they used the height of a cone where the slant height belonged.
So treat this chapter as a memory chapter with three decision points, not as a reasoning chapter. Point one: is the figure flat or solid? Point two: if solid, does the question want *volume*, *curved surface*, or *total surface*? Point three: is anything being melted, recast, painted or fenced — because that phrase alone tells you which of the three you need.
Get those three right and the arithmetic is a single substitution. Get them wrong and the perfectly correct arithmetic still lands on a wrong option, which is exactly what the paper-setter is counting on.
1. A cuboid measures 6 cm × 8 cm × 10 cm. What is the length of its longest diagonal?
2. Each side of a square is increased by 20%. By what percentage does its area increase?
3. A solid sphere of radius 3 cm is melted and recast into small cones, each of radius 1 cm and height 3 cm. How many such cones are obtained?
4. What is the total surface area of a solid hemisphere of radius 7 cm? (Take π = 22/7)
5. What is the area of an equilateral triangle whose side is 8 cm?
6. A room is 10 m long, 8 m wide and 4 m high. The cost of painting its four walls and the ceiling at ₹10 per square metre is:
7. If the radius of a sphere is increased by 10%, its volume increases by:
8. The diagonals of a rhombus are 16 cm and 12 cm. Its area is: