Volume of Cone Calculator Formula

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

Use the Volume of Cone Calculator

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

    Frequently Asked Questions

    How do you find the volume of a cone?

    Use V = (1/3)πr²h. It is exactly one-third of the volume of a cylinder with the same radius and height.

    What is slant height?

    Slant height is the distance from the tip (apex) of the cone to any point on the edge of the circular base, measured along the surface. It is calculated as l = √(r² + h²).

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