How to Calculate the Height of a Cone From the Volume

A cone is a 2-D geometric shape with a circular base. The sides of the cone slant inward as the cone grows in height to a single point, called its apex or vertex. Calculate the volume of a cone by its base and height with the equation volume = 1/3 * base * height. You can calculate the height of a cone from its volume by reversing this equation.

Things You'll Need

• Calculator

Instructions

1. Triple the volume amount. For this example, the volume is 100. Multiplying the volume by 3 results in 300.

2. Square the radius, and then divide the radius squared into the tripled volume. For this example, the radius is 2. The square of 2 is 4, and 300 divided by 4 is 75.

3. Divide the amount calculated in Step 2 by pi, which is an unending math constant that begins 3.14, to calculate the cone's height. For this example, 75 divided by pi results in 23.87. The height of this cone is 23.87.

References

• Wolfram MathWorld: Cone
• Math Expression: Volume of a Cone
• Israel Science and Technology Homepage: Formula for Geometric Figures

Resources

• Calculator Soup: Right Circular Cone Calculator