Master Volume & Surface Area from Zero

Volume is the amount of 3D space a shape occupies. Surface area is the total area of all faces. Common shapes: Cube, Cuboid, Cylinder, Cone, Sphere, Hemisphere.

Key Formulas

Cube

Volume=a³, Surface Area=6a², Diagonal=a√3

All sides equal.

Cylinder

Volume=πr²h, CSA=2πrh, TSA=2πr(r+h)

Most common 3D shape in exams.

Cone

Volume=πr²h/3, CSA=πrl (l=slant height)

l=√(r²+h²).

Sphere

Volume=4πr³/3, Surface Area=4πr²

Hemisphere: half of sphere.

⚡ Shortcut Tricks

1 litre = 1000 cm³ = 1000 mL.

Slant height l = √(r²+h²) for cone and pyramid.

If radius doubles, volume becomes 8 times.

Melted and recast — volume stays same.

✏️ Solved Examples

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