Questions
2 questions per paper
Difficulty
Medium
Importance
Medium yield for SSC/Bank exams
Overview
Mensuration is the branch of mathematics dealing with the measurement of lengths, areas, and volumes of geometric figures. It is a high-scoring section in SSC and banking exams, requiring a blend of memorized formulas and spatial visualization to solve within strict time constraints.
Area and Perimeter of 2D Figures
This section covers the quantitative assessment of boundaries and internal regions of polygons and circular shapes. Mastering these is foundational for solving more complex 3D surface area problems.
- Area of Triangle = 1/2 * base * height or sqrt(s(s-a)(s-b)(s-c)) [Heron's Formula]
- Area of Circle = πr^2; Circumference = 2πr
- Area of Parallelogram = base * height
- Area of Trapezium = 1/2 * (sum of parallel sides) * height
- Area of Rhombus = 1/2 * d1 * d2
Volume and Surface Area of 3D Solids
3D mensuration focuses on the capacity and surface coverings of solid objects. Exams frequently test your ability to relate these volumes when one shape is melted or recast into another.
- Volume of Cylinder = πr^2h; Total Surface Area = 2πr(r+h)
- Volume of Cone = 1/3 * πr^2h; Slant height l = sqrt(r^2+h^2)
- Volume of Sphere = 4/3 * πr^3; Surface Area = 4πr^2
- Volume of Cuboid = l * b * h; Diagonal = sqrt(l^2+b^2+h^2)
- Lateral Surface Area of Cube = 4a^2; Total Surface Area = 6a^2
Combined and Composite Figures
These questions involve objects formed by joining two or more basic solids, such as a tent (cylinder + cone) or a capsule (cylinder + two hemispheres). Speed-solving depends on identifying common dimensions shared between the shapes.
- Common interface area is subtracted from total surface area
- Volume of combined solid is the simple arithmetic sum of individual volumes
- Key strategy: Look for identical radii or heights in joined figures
- Frustum of a cone: V = 1/3 * πh(R^2 + r^2 + Rr)
- Area of paths inside or outside a rectangular field: 2w(l+b) ± 4w^2
Formula Sheet
Circle: Area = πr^2, Circumference = 2πr
Triangle: Area = 1/2*base*height
Rectangle: Area = l*b, Perimeter = 2(l+b)
Cuboid: Volume = l*b*h, TSA = 2(lb+bh+lh)
Cube: Volume = a^3, TSA = 6a^2
Cylinder: Volume = πr^2h, LSA = 2πrh
Cone: Volume = 1/3*πr^2h, CSA = πrl
Sphere: Volume = 4/3*πr^3, SA = 4πr^2
Hemisphere: Volume = 2/3*πr^3, TSA = 3πr^2
Exam Tip
Always keep your answer in terms of π until the final calculation to save time and prevent rounding errors before the last step.
Common Mistakes
- Confusing units of measurement (e.g., cm squared for area vs cm cubed for volume).
- Forgetting to exclude the base or overlapping faces when calculating the Total Surface Area of composite solids.
- Mistaking diameter for radius in circular formulas, leading to a factor of 4 error.
More Revision Notes
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