A cone is a three-dimensional structure or shape with circular base composition and a collection of line segments that link all of the points on the base to the apex. A cone consists of a non-congruent circular disc stacked on top of one another with the radius ratio of neighboring discs remaining constant and same. A cone can be thought of as a triangle with one of its vertices rotated. We can easily estimate the curved surface area and the total surface area of cone formula is done using a predefined set of formulas known as the cone formula.

## Types of Cone

**Right Circular Cone:** In this type of cone, the axis forms a right angle from the base.

Oblique Cone: In this type of cone, the axis is non-perpendicular to the base of the cone.

### Surface Area of Cone Formula

When we think of cones, we typically think of a right circular sphere. When you cut a paper cone in half and open it, you can see the outline of the paper that forms the cone’s surface. When the sides labeled P and Q are joined together, the curved portion of the shape forms a circle. In addition, if this form is cut into small pieces along the lines shown in the diagram, you’ll notice that the pieces form a triangle with a height equal to the slant height, l.

- The curved surface area of a cone is expressed as πrl
- Total surface area of a cone = πr(l+r)

Where r is the provided base radius, h is the height and l is the slant height of the respective cone.

#### Derivation of the Surface Area Formula

We divide a cone into a circular base and a top slanted component in order to measure the curved surface area and total surface area. The area of the slanted component determines the curved surface area, if you need more help check out Tutor Hunt for a math tutor near you. The sum of the circular base and curved surface areas is the total surface area.

##### Area of the Circular Base:

The base is a simple or standard circle and we know that area of a circle is expressed as:

Area of a circle = πr², where r is the provided base radius of the respective cone.

###### Area of Curved Surface

When we imagine opening the curved top and cutting it into small pieces so that each cut area is a small triangle, whose height is the slant height l of the respective cone.

###### Terms of a Cone

To make the calculation of the surface area and volume of a cone easier and accurate we first need to understand a few terms:

**Radius:**The radius provided is the distance from the center to the edge of the circle at the end.**Height:**The height provided is the distance from the center of the circle to the tip of the cone.**Slant:**The slant or the slope provided in a cone is the length from the edge of the circle to the tip.**Pi:**Pi is a special number or estimation we associate with circles. We will use an abbreviated version of Pi = 3.14. We also use the symbol π to refer to the number pi in formulas for calculation purposes.

###### Volume of Cone

Cones are three-dimensional triangles along with a circle-shaped base. According to the structure, composition, and properties, the volume of cone is expressed or represented as 1/3 of a cylinder with the same radius of base and height. As the widely used standard formula for the volume of a cylinder is πr²h, so, the volume of a Cone will be expressed as 1/3 πr²h where, r is the provided or given radius of the base and h is the height in the respective cone.

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