Cone Height

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Cone Height Calculation:

  •  r =

    Radius of the circular base of the cone

  •  V =

    Volume of the cone in cubic units

  •  h =

    Height from the base of the cone to the tip

  •

    Choose the number of decimals to show in your answer. This is also known as significant figures. Select an appropriate amount of significant figures based on the precision of the input numbers.

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Cone Height Formula

The height of a cone can be calculated if the volume and radius are known.

h = 3 * V / π * r2

Cone Height Variables

The height of a cone can be calculated if the volume and radius of the circular base are known.

Volume (V)
Known volume of the cone is cubic meters.
Radius (r)
Radius of the circular base of the cone in linear units.
Height (h)
Length from the center of the circular base to the tip of the cone at a right angle.

Cone Height Solution

How do we find the height of a cone with a volume of 45 and a radius of 3?

  • h = 3 * V / π * r2
  • substitute in the known values
  • h = 3 * 45 / π * 32
  • Find the height of a cone with volume 45 and radius 3
  • h = 3 * 45 / π * 9
  • Square the radius, 3 squared is 9
  • h = 135 / 28.27431
  • Multiply the numerator and denominator, π approximated to 3.14159 in example
  • h ≈ 4.77465
  • Divided numerator by denominator
  • 4.775
  • Rounded the answer to three decimal places

The height of a cone with a volume of 45 and a radius of 3 is approximately 4.775 linear units

Need help converting volume to other units?

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