Chapter 21 of 31

Mensuration (2D & 3D)

Area, perimeter, volume and surface area formulas for every standard 2D and 3D shape — organised for quick recall.

📖 ~4 min read 📐 RRB NTPC / Group D — Mathematics

2D Shapes

ShapeAreaPerimeter
Squareside²4×side
Rectanglelength×breadth2(length+breadth)
Triangle½×base×heightsum of sides
Circleπr²2πr

3D Shapes

ShapeVolumeTotal Surface Area
Cubeside³6×side²
Cuboidl×b×h2(lb+bh+hl)
Cylinderπr²h2πr(r+h)
Cone⅓πr²hπr(r+l), l=slant height
Sphere4/3 πr³4πr²
⚠️ Total Surface Area includes ALL faces (top/bottom too); Curved Surface Area excludes flat top/bottom.
💡 Example: Cylinder radius 7cm, height 10cm (π=22/7) → Volume = 22/7 × 49 × 10 = 1,540 cm³

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