3D Mensuration
1. Cube
- Volume: a³ (where a = side)
- Total Surface Area: 6a²
- Lateral Surface Area: 4a²
- Diagonal: a√3
2. Cuboid
- Volume: l × b × h
- Total Surface Area: 2(lb + bh + hl)
- Lateral Surface Area: 2h(l + b)
- Diagonal: √(l² + b² + h²)
3. Cylinder
- Volume: πr²h
- Curved Surface Area: 2πrh
- Total Surface Area: 2πr(r + h)
- r = radius, h = height
4. Cone
- Volume: (1/3)πr²h
- Curved Surface Area: πrl
- Total Surface Area: πr(r + l)
- Slant height (l): √(r² + h²)
5. Sphere
- Volume: (4/3)πr³
- Surface Area: 4πr²
6. Hemisphere
- Volume: (2/3)πr³
- Curved Surface Area: 2πr²
- Total Surface Area: 3πr²
7. Frustum of Cone
- Volume: (1/3)πh(r₁² + r₂² + r₁r₂)
- Curved Surface Area: πl(r₁ + r₂)
- r₁, r₂ = radii, h = height, l = slant height
Quick Tips
- Cube is special case of cuboid
- Cone volume is 1/3 of cylinder
- Sphere volume uses 4/3, hemisphere uses 2/3
- Always check units (convert if needed)