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Mensuration 3D (Volume & Surface Area)

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Sniper Mode: Solid Objects

1. Cube & Cuboid

  • Cuboid:
    • Volume = L x B x H.
    • TSA (Total Surface Area) = 2(LB + BH + HL).
    • Diag (Longest Rod) = тИЪ(L┬▓+B┬▓+H┬▓).
  • Cube:
    • Vol = a┬│.
    • TSA = 6a┬▓.
    • Diag = aтИЪ3.

2. Cylinder & Cone

  • Cylinder:
    • Vol = ╧Аr┬▓h.
    • CSA (Curved Surface) = 2╧Аrh.
    • TSA = 2╧Аrh + 2╧Аr┬▓ = 2╧Аr(h+r).
  • Cone:
    • Vol = (1/3)╧Аr┬▓h.
    • Slant Height (l) = тИЪ(h┬▓+r┬▓).
    • CSA = ╧Аrl.
    • TSA = ╧Аr(l+r).

3. Sphere & Hemisphere

  • Sphere:
    • Vol = (4/3)╧Аr┬│.
    • Surface Area = 4╧Аr┬▓.
  • Hemisphere:
    • Vol = (2/3)╧Аr┬│.
    • CSA = 2╧Аr┬▓.
    • TSA = 3╧Аr┬▓ (Flat face added).

4. Melting & Recasting

  • Volume remains CONSTANT.
  • N Small balls = Big Sphere Vol / Small Sphere Vol.
  • N = (R/r)┬│ for Spheres/Cubes.