Mensuration — Areas, Volumes & Surface Areas Made Simple
A clear guide to 2D area and perimeter and 3D volume and surface-area formulas — squares, circles, cuboids, cylinders, cones and spheres — for SSC-CGL.
By the PadhoDost Team · 📖 7 min read · Updated 4 August 2026
Part of SSC CGL & Banking prep🧠 Painting vs Filling a Water Tank
Imagine a closed water tank. How much paint you need to coat its outside is surface area. How much water it can hold inside is volume. Mensuration is just measuring these two things — the skin and the stuffing — for every shape you meet.
Shapes come in two families. Flat 2D shapes (square, rectangle, triangle, circle) have area (space inside) and perimeter (boundary length). Solid 3D shapes (cube, cuboid, cylinder, cone, sphere) have volume (space they occupy) and surface area (total outer covering). Learn the formulas family-by-family and the topic becomes pure substitution.
2D Shapes — Area & Perimeter
| Shape | Area | Perimeter / Boundary |
|---|---|---|
| Square (side a) | a^2 | 4a |
| Rectangle (l, b) | l x b | 2(l + b) |
| Triangle (base b, height h) | 1/2 x b x h | sum of three sides |
| Circle (radius r) | pi x r^2 | 2 x pi x r |
3D Solids — Volume & Surface Area
| Solid | Volume | Surface Area |
|---|---|---|
| Cube (side a) | a^3 | TSA = 6a^2 |
| Cuboid (l, b, h) | l x b x h | TSA = 2(lb + bh + hl) |
| Cylinder (r, h) | pi x r^2 x h | CSA = 2 pi r h; TSA = 2 pi r (r + h) |
| Cone (r, h) | 1/3 x pi x r^2 x h | CSA = pi r l; TSA = pi r (r + l) |
| Sphere (r) | 4/3 x pi x r^3 | 4 x pi x r^2 |
📝 A cylinder, fully solved
Find the volume, curved surface area (CSA) and total surface area (TSA) of a cylinder with radius r = 7 cm and height h = 10 cm. Take pi = 22/7.
Volume = pi x r^2 x h = (22/7) x 7 x 7 x 10 = 22 x 7 x 10 = 1540 cubic cm.
CSA = 2 x pi x r x h = 2 x (22/7) x 7 x 10 = 2 x 22 x 10 = 440 square cm.
TSA = 2 x pi x r x (r + h) = 2 x (22/7) x 7 x (7 + 10) = 2 x 22 x 17 = 748 square cm.
Notice the 7 in the radius cancels the 7 in 22/7 every time — that is why pi = 22/7 was chosen.
How to solve any mensuration sum
- 1Identify the shape and whether the question asks for area/perimeter (2D) or volume/surface area (3D).
- 2List the given values and make sure all are in the same unit.
- 3Pick the exact formula from the table and substitute carefully.
- 4For circles and rounded solids, choose pi = 22/7 or 3.14 based on the numbers given.
- 5Attach the correct unit: square units for area/surface, cubic units for volume.
Lock these in
- ✓Area and surface area are in square units; volume is in cubic units.
- ✓Circle area = pi r^2, circumference = 2 pi r — do not mix them up.
- ✓Cylinder: Volume = pi r^2 h, CSA = 2 pi r h, TSA = 2 pi r (r + h).
- ✓Sphere: Volume = 4/3 pi r^3, Surface = 4 pi r^2.
- ✓Cone needs slant height l = root of (r^2 + h^2) for its CSA = pi r l.
⚡ Quick check
What is the area of a circle whose radius is 7 cm? (Take pi = 22/7)
Ready to test yourself? 🎯
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