Mensuration
Learning Objectives
- Understand the fundamental concepts of Mensuration
- Apply key formulas and techniques to solve problems
- Practice with exam-level questions to build speed and accuracy
Key Concepts
What is Mensuration?
Mensuration deals with the measurement of geometric figures — their area, perimeter, surface area, and volume. SSC CGL Tier 1 typically asks 2-3 questions from this topic covering 2D shapes (triangles, circles, rectangles) and 3D shapes (cubes, cylinders, cones, spheres).
Key Concepts
1. 2D Shapes: Area of triangle = (1/2) * base * height. Area of circle = pi*r^2. Circumference = 2*pi*r. Area of rectangle = l * b. Area of square = side^2. Area of trapezium = (1/2) * (sum of parallel sides) * height.
2. 3D Shapes: Volume of cube = side^3. Surface area = 6 * side^2. Volume of cuboid = l * b * h. Volume of cylinder = pi*r^2*h. Curved surface area = 2*pi*r*h. Volume of cone = (1/3)*pi*r^2*h. Volume of sphere = (4/3)*pi*r^3. Surface area = 4*pi*r^2.
3. Combined & Hollow Shapes: Volume of hollow cylinder = pi*h*(R^2 - r^2). Volume of frustum of cone = (1/3)*pi*h*(R^2 + r^2 + Rr).
4. Heron Formula: For a triangle with sides a, b, c: semi-perimeter s = (a+b+c)/2. Area = sqrt[s(s-a)(s-b)(s-c)].
Solved Examples
a) 616 cm^2 b) 628 cm^2 c) 640 cm^2 d) 656 cm^2
a) 1440 cm^3 b) 1540 cm^3 c) 1600 cm^3 d) 1650 cm^3
a) 64 cm^2 b) 74 cm^2 c) 84 cm^2 d) 94 cm^2
Shortcut Techniques
- Use pi = 22/7 or 3.14 based on the numbers. If radius is a multiple of 7, use 22/7 for exact calculation.
- For area of equilateral triangle, use sqrt3/4 * side^2. sqrt3 approx = 1.732.
- Surface area to volume ratio decreases as size increases. This helps in checking answers for similar shapes.
- For combined solids, add individual volumes but be careful with surface areas — common faces are not counted.
Advanced Applications
Modern exams feature questions combining multiple quantitative concepts. Master these by practicing previous year papers.
Shortcut Methods
Percentages: Use fraction table (12.5%=1/8, 20%=1/5, 25%=1/4). SI/CI: For 2 years, CI-SI = P(r/100)^2. Time Work: Use LCM of time periods. Average Speed: 2ab/(a+b) for equal distances.
Advanced Applications
Modern exams feature questions combining multiple quantitative concepts. Master these by practicing previous year papers.
Shortcut Methods
Percentages: Use fraction table (12.5%=1/8, 20%=1/5, 25%=1/4). SI/CI: For 2 years, CI-SI = P(r/100)^2. Time Work: Use LCM of time periods. Average Speed: 2ab/(a+b) for equal distances.
Advanced Applications
Modern exams feature questions combining multiple quantitative concepts. Master these by practicing previous year papers.
Shortcut Methods
Percentages: Use fraction table (12.5%=1/8, 20%=1/5, 25%=1/4). SI/CI: For 2 years, CI-SI = P(r/100)^2. Time Work: Use LCM of time periods. Average Speed: 2ab/(a+b) for equal distances.
Advanced Applications
Modern exams feature questions combining multiple quantitative concepts. Master these by practicing previous year papers.
Shortcut Methods
Percentages: Use fraction table (12.5%=1/8, 20%=1/5, 25%=1/4). SI/CI: For 2 years, CI-SI = P(r/100)^2. Time Work: Use LCM of time periods. Average Speed: 2ab/(a+b) for equal distances.