Questions
3 questions per paper
Difficulty
Medium
Importance
Medium yield for ONGC/BHEL/IOCL
Overview
Geometry and Mensuration form the backbone of quantitative aptitude in PSU examinations, requiring a strong command over spatial reasoning and formula application. Mastering the properties of polygons, circles, and 3D solids is essential for securing quick marks in technical screening tests.
Area & Perimeter of 2D Figures
This section covers the boundaries and interior space of basic polygons. Understanding how perimeter and area scale relative to side length changes is a common focus in PSU speed tests.
- Rectangle: Area = l * b, Perimeter = 2(l + b)
- Square: Area = side^2, Perimeter = 4 * side
- Trapezium: Area = 0.5 * (sum of parallel sides) * height
- Rhombus: Area = 0.5 * d1 * d2
- Area of regular polygon = (n * s^2) / (4 * tan(pi/n))
Triangles & Circles
Properties of triangles, including concurrency points and circle theorems, frequently appear in questions involving nested figures. Focus on the relationship between radius, chord length, and triangle interior angles.
- Area of triangle = 0.5 * base * height
- Heron's Formula: Area = sqrt(s(s-a)(s-b)(s-c)) where s = semi-perimeter
- Circle: Area = pi * r^2, Circumference = 2 * pi * r
- Angle at the center is double the angle at the circumference
- Pythagoras Theorem: a^2 + b^2 = c^2 for right triangles
Volume & Surface Area of 3D Solids
3D mensuration involves calculating the total surface area, lateral surface area, and volume of solids. Questions often involve melting one shape to cast another, where volume remains constant.
- Cube: Volume = a^3, TSA = 6a^2
- Cylinder: Volume = pi * r^2 * h, CSA = 2 * pi * r * h
- Cone: Volume = (1/3) * pi * r^2 * h
- Sphere: Volume = (4/3) * pi * r^3, Surface Area = 4 * pi * r^2
- Slant height of cone (l) = sqrt(r^2 + h^2)
Coordinate Geometry Basics
This subtopic explores the algebraic representation of geometric shapes in a 2D plane. PSU exams often ask for distances, midpoints, and the slopes of lines passing through specific coordinates.
- Distance between (x1, y1) and (x2, y2) = sqrt((x2-x1)^2 + (y2-y1)^2)
- Midpoint formula: ((x1+x2)/2, (y1+y2)/2)
- Slope (m) = (y2-y1) / (x2-x1)
- Equation of line: y = mx + c
- Section formula: ((mx2 + nx1)/(m+n), (my2 + ny1)/(m+n))
Formula Sheet
Area = l * b
Area = 0.5 * b * h
Heron's Formula: sqrt(s(s-a)(s-b)(s-c))
Area of Circle = pi * r^2
Volume of Cylinder = pi * r^2 * h
Volume of Cone = (1/3) * pi * r^2 * h
Volume of Sphere = (4/3) * pi * r^3
Distance Formula = sqrt((x2-x1)^2 + (y2-y1)^2)
Slope = (y2-y1)/(x2-x1)
Exam Tip
Always visualize the 2D cross-section if a 3D geometry question seems complex; it often simplifies the problem into basic trigonometry or Pythagorean relations.
Common Mistakes
- Confusing the lateral surface area with total surface area in 3D problems.
- Forgetting to convert units (e.g., cm to m) before calculating area or volume.
- Misidentifying the diameter for the radius in circle and sphere calculations.
More Revision Notes
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