Questions
~2 questions per exam
Difficulty
Medium
Importance
Low weightage but essential for score optimization
Overview
Mensuration and probability are essential quantitative aptitude modules that test spatial geometry visualization and logical reasoning under time constraints. Mastering these topics ensures you can quickly solve questions regarding shape dimensions, surface areas, volumes, and likelihood of events, which frequently appear as low-to-medium difficulty anchors in competitive exams.
Mensuration: 2D Plane Figures
2D mensuration involves calculating the perimeter and area of flat geometric shapes. Competitive exams often test your ability to handle composite figures or relate changes in dimensions to percentage changes in area.
- Rectangle: Area = l * b, Perimeter = 2(l + b)
- Square: Area = a^2, Diagonal = a√2
- Triangle: Area = (1/2) * base * height
- Equilateral Triangle: Area = (√3/4) * a^2
- Circle: Area = πr^2, Circumference = 2πr
- Rhombus: Area = (1/2) * d1 * d2
Mensuration: 3D Solid Figures
3D mensuration focuses on total surface area, lateral surface area, and volume calculation. Efficiency is gained by memorizing volume ratios and understanding cross-sectional changes during melting and recasting problems.
- Cube: Volume = a^3, TSA = 6a^2
- Cuboid: Volume = l * b * h, TSA = 2(lb + bh + lh)
- Cylinder: Volume = πr^2h, CSA = 2πrh
- Cone: Volume = (1/3)πr^2h, LSA = πrl (l = √(r^2+h^2))
- Sphere: Volume = (4/3)πr^3, SA = 4πr^2
Probability: Fundamental Concepts
Probability measures the uncertainty of outcomes in an experiment. In competitive exams, questions usually revolve around simple coin flips, dice rolls, and card selection tasks.
- P(E) = n(E) / n(S)
- P(not E) = 1 - P(E)
- P(A or B) = P(A) + P(B) - P(A and B)
- For independent events: P(A and B) = P(A) * P(B)
- Total outcomes for n dice: 6^n
- Total outcomes for n coins: 2^n
Formula Sheet
Area of Trapezium = (1/2) * (sum of parallel sides) * height
Volume of Hemisphere = (2/3)πr^3
TSA of Cylinder = 2πr(h + r)
P(E) = Favorable Outcomes / Total Sample Space
nCr = n! / (r! * (n - r)!)
Slant height of cone (l) = √(r^2 + h^2)
Exam Tip
In mensuration problems, focus on the units and the ratio of dimensions first; often, the answer can be eliminated by checking units without completing the full calculation.
Common Mistakes
- Confusing Total Surface Area (TSA) with Curved/Lateral Surface Area (CSA/LSA) in 3D formulas.
- Forgetting to convert units (e.g., cm to m) before performing calculations in mensuration.
- Miscalculating combinations in probability, specifically failing to account for 'with replacement' versus 'without replacement' scenarios.
More Revision Notes
Ready to test yourself?
Play topic-wise Mensuration & Probability questions in Aspirant Arcade — gamified MCQ practice.
Download Free