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3D Shape Solver

Volume of a Cone

Instantly calculate the magnitude, slant height, and total surface area of a right circular cone.

Volume
1/3 Cylinder
Slant Height
Calculated
units
units

Cone Formulas

A cone is a 3D shape that tapers smoothly from a flat circular base to a point called the apex.

Volume Formula

V = (1/3) × π × r² × h

Total Surface Area

A = πr(r + s)

where s is slant height

Slant Height (s)

s = √(r² + h²)

Calculated using Pythagoras theorem.

How to Calculate Cone Volume

The volume of a cone is exactly one-third the volume of a cylinder with the same radius and height.

  1. Square the radius: Multiply the radius by itself (r × r).
  2. Multiply by height: Multiply the result by the height (h).
  3. Multiply by Pi: Multiply by π (3.14159).
  4. Divide by 3: Finally, divide the total by 3.

Frequently Asked Questions

What is slant height?

The slant height is the distance from the outer edge of the base to the apex (tip) of the cone. It is always longer than the vertical height.

Can I calculate volume with just radius and slant height?

Yes, but you first need to find the vertical height using Pythagoras theorem: h = √(s² - r²).