Cone Volume & Surface Area Calculator Formula

Understand the math behind the cone volume & surface area calculator. Each variable explained with a worked example.

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Formulas Used

Volume

volume = (1/3) * pi * pow(r, 2) * h

Lateral Sa

lateral_sa = pi * r * slant

Total Sa

total_sa = pi * r * slant + pi * pow(r, 2)

Slant Height

slant_height = slant

Variables

VariableDescriptionDefault
rBase Radius4
hHeight9
slantDerived value= sqrt(pow(r, 2) + pow(h, 2))calculated

How It Works

Cone Formulas

Volume

V = (1/3) × pi × r² × h

Slant Height

l = sqrt(r² + h²)

Surface Area

  • Lateral area = pi × r × l
  • Total area = pi × r × l + pi × r² = pi × r × (l + r)

    • Worked Example

    Cone with radius 4 and height 9.

    r = 4h = 9
    1. 01Slant = √(16+81) = √97 ≈ 9.8489
    2. 02Volume = (1/3)×pi×16×9 = 48pi ≈ 150.7964
    3. 03Lateral SA = pi×4×9.8489 ≈ 123.7168
    4. 04Total SA = 123.7168 + pi×16 ≈ 173.9460

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