Volume of Cone Calculator Formula

Understand the math behind the volume of cone calculator. Each variable explained with a worked example.

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Formulas Used

Volume

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

Lateral Area

lateral_area = pi * r * slant_height

Total Surface Area

total_surface_area = pi * r * slant_height + pi * r^2

Slant

slant = slant_height

Base Area

base_area = pi * r^2

Variables

VariableDescriptionDefault
rRadius3
hHeight8
slant_heightDerived value= sqrt(r^2 + h^2)calculated

How It Works

How to Calculate the Volume of a Cone

Formula

V = (1/3) × π × r² × h

A cone has exactly 1/3 the volume of a cylinder with the same base and height.

Where:

  • V = Volume
  • π ≈ 3.14159
  • r = radius of the base
  • h = height

    • Slant Height

    l = √(r² + h²)

    Surface Area

  • Lateral area = πrl (the curved surface)
  • Total area = πrl + πr² (curved surface + base)

    • Worked Example

    Find the volume of a cone with radius 3 and height 8.

    r = 3h = 8
    1. 01V = (1/3) × π × 3² × 8
    2. 02= (1/3) × π × 9 × 8
    3. 03= (1/3) × 72π
    4. 04= 24π
    5. 05≈ 75.3982
    6. 06Slant height = √(9 + 64) = √73 ≈ 8.5440

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