Cone Height Formula
A cone is a threedimensional shape, formed by using a set of line segments or the lines which connect at a common point, called the apex or vertex, to all the points of a circular base(which does not contain the apex). We can also define the cone as a pyramid with a circular crosssection, unlike a pyramid that has a triangular crosssection. Let us study the cone height formula using solved examples at the end of the page.
What Is Cone Height Formula?
The cone height formula helps in calculating the distance from the vertex of the cone to the cone's base. Cone Height Formula for Cone can be expressed as,
h = 3V/πr^{2}
where,
 V = Volume of a cone
 R = Radius of a cone
This formula is derived from the formula of the volume of a cone. Let us see the applications of the cone height formula in the following section.
Solved Examples Using Cone Height Formula

Example 1: A birthday cap is in conical shape having a volume of 20 units^{3} and its base radius is 5 units. What is the height of a cap?
Solution:
To find: The height of a cone.
Given:
volume = 20 units^{3}
Radius = 5 units
Using cone height formula,
h = 3V/πr^{2}
= (3 × 20)/π × 5^{2}
= (60)/ (π × 25)
= 0.76 units
Answer: The height of a cone is 0.76 units

Example 2: What is the height of the cone with the radius = 3 units and volume = 50 cubic units?
Solution:
To find: The height of a cone.
Given:
volume = 50 cubic units
Radius = 3 units
Using cone height formula,
h = 3V/πr^{2}
= (3 × 50)/π × 3^{2}
= (150)/ (π × 9)
= 5.305 units
Answer: The height of a cone is 5.305 units.