A right circular cone is a geometric shape with a circular base and one vertex that is perpendicular to the base. The shape is formed by connecting all of the points along the circle’s circumference to the vertex. The properties of a right circular cone are somewhat unique from other shapes, including other conic sections such as ellipses or parabolas. This uniqueness makes it useful in many fields, including architecture, mechanical engineering, and manufacturing. The mathematical definition for a right circular cone can be found below.

## What is a right circular cone?

A right circular cone is a three-dimensional shape that has a circular base and a curved surface. It is also known as a solid figure, which means that it has volume, height, and other measurable characteristics.

A right circular cone can be described as being similar to an upside down pyramid with its vertex pointing upwards rather than downwards. You may have seen this type of shape in everyday life; for example, when you see certain types of cans or bottles. They have this exact same shape!

The sides (or lateral surfaces) of the right circular cone are perpendicular to each other at their meeting point on top where they touch together to form what we call “a vertex”.

## Right circular cone properties

A right circular cone is a solid figure with a circular base and a straight side that extends upwards from the circular base. It is called such because if one were to slice through the cone at an angle parallel to its axis, it would form two identical halves, each of which are the same shape as cones: a cylinder and a pyramid. The length of this side is called its height, h.

## Volume of a right circular cone

The formula for the volume of a right circular cone is:

V = \frac {\pi \times r^2 \times h}{3}

where “V” represents volume and “r” represents radius, which is the distance from the center of the circle to a point on its circumference. The height is equal to the distance from any point on the base of an inscribed cylinder to its vertex (a vertex being where two planes meet at an angle), or in other words, how high it sticks up above its base.

## Surface area of a cone

The lateral surface area of a right circular cone is the sum of all the areas between the base and lateral surface.

The base is the part of the cone that lies directly below it’s apex. There are two types of bases: circular and non-circular (i.e., rectangular).

The lateral surface area is all sides except for its base; it’s also called flanks or sides. The lateral surface consists of both ends: top and bottom.

## How to use the right circular cone calculator

With our right circular cone calculator, as long as you know the radius and the height, you can calculate:

• The circumference of the base
• The slant height
• The surface area
• The volume
• The lateral surface area
• The base area

There is also an advanced mode, which shows you all the formulas, if you want to be more intricate.

## FAQ

### How many bases does a cone have?

A cone has one base.

### What is a right circular cone?

A right circular cone is a three-dimensional shape that has a circular base and a curved surface.

### How do you calculate the volume of a right circular cone?

You can use the formula: V = 1/3 x pi x r^2 x h.