Mensuration — area and volume
Key facts
- Perimeter is measured in linear units such as cm or m, while area is measured in square units such as cm^2 or m^2.
- Volume is measured in cubic units such as cm^3 or m^3, so unit form is a quick option-check in MCQs.
- The cylinder example with r = 7 cm, h = 10 cm and pi = 22/7 gives volume 1540 cm^3 and curved surface area 440 cm^2.
- Pythagoras and standard triples such as 3-4-5, 5-12-13 and 8-15-17 often provide the missing side before an area or cone formula is used.
- Rajasthan's area of 3,42,239 sq km is a scale-based reminder that map area and real area questions require correct units.
Key Points at a Glance
- 1
Mensuration first separates boundary length, flat coverage, outer covering and solid capacity.
- 2
Perimeter is measured in linear units such as cm or m, while area is measured in square units such as cm^2 or m^2.
- 3
Volume is measured in cubic units such as cm^3 or m^3, so unit form is a quick option-check in MCQs.
- 4
Square, rectangle, triangle, circle, rhombus and trapezium questions usually test direct formula selection.
- 5
Cube, cuboid, cylinder, cone, sphere and hemisphere questions usually test surface area versus volume.
- 6
The cylinder example with r = 7 cm, h = 10 cm and pi = 22/7 gives volume 1540 cm^3 and curved surface area 440 cm^2.
- 7
Pythagoras and standard triples such as 3-4-5, 5-12-13 and 8-15-17 often provide the missing side before an area or cone formula is used.
- 8
Rajasthan's area of 3,42,239 sq km is a scale-based reminder that map area and real area questions require correct units.
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Mensuration basics
Mensuration is the part of mathematics that measures shapes. In objective recruitment exams, the first step is not calculation but classification: is the question asking for a boundary, a covered flat region, an outer surface, or a solid capacity? Perimeter is boundary length. Area is the region inside a plane figure. Surface area is the covering over a three-dimensional solid. Volume is the capacity or space occupied by that solid.
This distinction prevents the most common MCQ error: using a correct formula for the wrong quantity. A path around a field asks for perimeter, not area. Painting a wall asks for area, not perimeter. Wrapping a box asks for surface area. Filling a tank asks for volume. The same numbers can appear in all four cases, so the noun in the question decides the formula before arithmetic starts.
The question language also tells you whether to add, subtract or keep one figure separate. A boundary around a rectangle, a circular track, the covered face of a wall and the capacity of a tank are not interchangeable situations. Read the object first, then read the dimensions.
Exam takeaway: mark the requested quantity first, then choose the formula.
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