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Quantitative Aptitude›Ch 4: Algebra, Geometry & Mensuration›Mensuration 3D: Volume & Surface Area
Master formulas and quick concepts for SSC, Railway and Defence exams
Total surface area covers all exposed faces including base and top, whereas curved surface area includes only lateral walls. Volume measures total internal space occupied by the 3D solid body.
Quick Memory Hooks
| Shape | Curved Surface Area | Volume |
|---|---|---|
| Cube (a) | 4a² | a³ |
| Cylinder (r, h) | 2πrh | πr²h |
| Cone (r, l, h) | πrl | ⅓πr²h |
| Sphere (r) | 4πr² (TSA) | ⁴/₃πr³ |
Cuboid
(Length, width, height)
Length, width, height
A standard matchbox represents a cuboid.
Cylinder
(Circular parallel bases)
Circular parallel bases
Water pipes and LPG cylinders are cylindrical.
Cone
(Slant height and apex)
Slant height and apex
A birthday cap is a classic cone example.
Hemisphere
(Half sphere with flat top)
Half sphere with flat top
A bowl filled with water is hemispherical.
Using diameter instead of radiusAlways divide diameter by 2 first
Radius is half of diameter. Forgetting this halves your score.
Confusing CSA and TSA of hemisphereHemisphere TSA is 3πr², CSA is 2πr²
A hemisphere has an extra circular flat base adding πr².
Forgetting slant height formula in conel = √(r² + h²)
Pythagoras theorem is needed to find slant height before CSA.
Q1.Find the volume of a cylinder with radius 7 cm and height 10 cm. (Use π = 22/7)
Q2.What is the total surface area of a solid hemisphere of radius 7 cm? (Use π = 22/7)