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Cone Calculator

Compute slant height, base area, lateral area, total surface area, and volume of a right circular cone.

Cone formulas

Slant heightl = √r2 + h2
VolumeV = 13πr2h
Lateral areaL = πrl
Total surface areaSA = πr(r + l)

Where r = base radius, h = vertical height, l = slant height

Worked examples

  1. A cone has radius 3 and height 4. Find the slant height, volume and surface area.

    1. l = √9 + 16 = 5
    2. V = 13π × 9 × 4 = 12π
    3. L = π × 3 × 5 = 15π
    4. SA = π × 3 × (3 + 5) = 24π

    Answer: l = 5, V ≈ 37.70, L ≈ 47.12, SA ≈ 75.40

Tips & common mistakes

  • A cone holds exactly one third of a cylinder with the same base and height.