# Surface Area of a Cone: Formula, Example and Definition

## In this article, we’ll look at the formula for the surface area of a cone using examples. Let’s get started.

KAMPALA | LIFESTYLE UGANDA (https://lifestyleuganda.com/) — A three-dimensional form is a solid object that has depth or height. Three-dimensional objects include the sphere, cuboid, cone, and so on.

three-dimensional shape’s surface area is the sum of the surface areas of all of its sides. Children will associate the form with a birthday present and the surface area with gift wrapping paper.

We will look at the surface area of a cone formula with examples in this article. Let’s get started.

## So what exactly is a cone?

It is a three-dimensional figure that exists in two forms: oblique and right circular cones. The difference between both is such that in the right circular cone, the vertex is above the centre of the base, and in the oblique cone, the vertex is not at the mentioned place.

So in this topic, we are going to read about the surface area of the cone. Let’s learn two ways by which you can find the surface area of the cone.

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## Definition of Surface Area of Cone

The surface area of a cone is the amount of space filled by the cone’s surface. This signifies that the base is composed of a radius or diameter.

The height of the cone is the distance between the centre of the base and the tallest section of the cone (in the case of ice cream, this area is at the bottom).

The surface area of a cone is filled by the surface/boundary of a cone. It is usually expressed as a square unit.

A cone is formed by stacking numerous triangles and rotating them around one axis. It has a total surface area as well as a curved surface area. This is so because it has a flat base.

## Surface Area in Simple Terms

When calculating the surface area of a 3-D form, imagine unfolding or flattening the shape and then calculating the area of each side.

The surface area of any given cone is calculated by adding all of these areas together.

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To find the area of a 3-D form, we must first know how to find the area of the fundamental shapes that make up the 3-D shape’s sides.

## Types of Surface Area of Cones

Curved Surface Area of a Cone

The curved surface area (CSA) of a figure-like cone is calculated with the given formula: Multiply π with radius and length.

CSA = πrl

In this case, r = the radius of the cone’s circular base, l = Cone’s slant height. When the cone is in the shape of a flat region (unrolled), l is the length of the arc of a sector and r is the radius of the sector.

Total Surface Area of Cones

The total surface area of a cone is known with the formula given below. It is the area filled by the cone in three dimensions. It equals the sum of the curved surface and the cone’s base.

The formula for calculating a cone’s total surface area is as follows:

Total Surface Area (TSA) = CSA + Circular Base Area

TSA = π*r*(r + l)

## What is the Volume of the cone?

The volume of a cone mentions a cone’s area or space. It can also be stated as the capacity of the figure – cone. A cone is a geometric figure with a base that is circular.

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The base of a cone originates from the base (flat in shape) to the vertex or apex.

A cone is made up of a series of line segments, half-lines, or lines that link a common point, the apex, to all the points on a base that are on a plane that does not include the apex.

A cone is defined as a collection of non-congruent circular discs that are piled on top of one another in such a way that the radius ratio of neighbouring discs remains constant.

If you want to learn more about the topic in detail and in a fun and interesting way, visit Cuemath. #### Ass. Editor

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