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Home > News & Articles > Surface Area of a Cone: Definitions, Examples, Formula, Height and Radius, Right Circular Cone, and Derivations
Updated on 12th June, 2023 , 4 min read
A three-dimensional form is one that has height or depth. Three-dimensional objects include the sphere, cuboids, cones, and so on. A three-dimensional shape's surface area is the sum of the surface areas of all of its sides. A cone is a three-dimensional shape with a circular base.
Cones are circular pyramid-like constructions with a circular base. It has a three-dimensional form with a smooth base that tapers at the highest point, known as the vertex. We assume a right circular cone with a circular base while analyzing the surface area of cones. A cone may be thought of as a triangle that has one of its vertices rotated.
What is the Surface Area?
When determining the surface area of a 3-D object, think about unfolding or flattening the shape and then computing the area of each side. All of these regions are added together to determine the surface area. Square units like square meters, square centimeters, or equivalents are used to measure surface areas. There are two types of surface areas-
The surface area of a cone is the area filled by the surface/boundary of a cone. It is usually expressed as a square unit. A cone is formed by stacking multiple triangles and spinning them around one axis. It has a total surface area as well as a curved surface area because it has a flat base. A cone can be classified as either a right circular cone or an oblique cone. In a right circular cone, the vertex is normally vertically above the center of the base, but in an oblique cone, the vertex is not vertically above the center of the base.
What is the Surface Area of a Cone Formula?
Where r is the radius of the circular base, the circumference of the cone's base equals 2πr. Therefore,
We are aware that a right-angled triangle can be rotated to form a cone. Using the following formula of Pythagoras' Theorem which enables to determine the length of the slant side of a right-angled triangle-
The overall surface area of the cone is equal to the sum of the curved surfaces plus the circumference of the base. Therefore, a cone's total surface area = πr² + πrl
Using r as the common value, we have,
Where,
I = Slant height
r = The base circle's radius
SA = Total surface area
h = Height of cone
It is also possible to write the CSA formula for a right circular cone as follows-
The radius of a sector with a radius equal to the slant height 'l' is equal to the area of a cone's curved surface. Thus, by Pythagoras' theorem, l² = r² + h²
The total surface area of a cone formula = the sum of its curved surface area and its circular base area (sector's area).
A cone's total surface area = πr² + πrl
Therefore,
Read more about the Maths Formulas.
Consider a cone to be a triangle that has one of its vertices rotated. Consider a scenario in which we need to paint the faces of a conical flask. Before we begin painting, we must determine the amount of paint necessary to cover all of the walls. To estimate the amount of paint needed, we need to know the area of each face of the container, which is known as the total surface area. A cone's total surface area is the sum of the areas of its faces. Let's create a universal cone formula to compute a cone's surface area.
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By - Nikita Parmar 2023-08-25 09:48:44 , 11 min readAns. A cone’s slant height is determined using the formula s=√(r² + h²) units, where "r" is the radius and "h" is the height.
Ans. The area of a cone’s curved surface is known as its curved surface area. The formula for calculating the curved surface area of a cone is rl, where ’r’ is the radius of the base and ’l’ is the cone’s slant height. We do not take into account the area of the cone’s base, which is shaped like a circle, in our calculation.
Ans. The area occupied by the surface of a cone is referred to as the cone’s surface area. A cone’s surface area may be divided into two types: total surface area and curved surface area.
Ans. Since a cone’s flat surface is circular, the formula for its flat surface is r² square units. The base surface area of a cone is another name for it.
Ans. The surface area of a cone is the space that its surface occupies in three dimensions. It is equal to the total of the lateral and base areas of the cone.
Ans. Because a cone’s flat surface is circular, the formula for the cone’s flat surface is πr² square units. It is also known as a cone’s base surface area.
Ans. A cone’s total surface area is equal to the sum of the base area and the curved surface area. The following formula is used to compute the cone’s full surface area- TSA of a cone is ᴨr² + ᴨrl = ᴨr (l + r) square units.
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