Cone-Curved Surface Area

The curved surface of a cone is the entire area covered by the surface of a cone. A cone is a 3D shape that has a circular base. The base consists of diameter and radius. The distance covered between the centre of the base and its topmost part is considered the height of the cylinder. When the surface area of a cone is concerned, it has two types of surface area named total surface area and curved surface area.   

Definition for the curved surface area of a cone.

Cone has two different types of surface area. One is regarded as the curved surface area and the other one is the total surface area. The curved surface area is regarded as the total area covered by the entire 3D structure of the cone. In order to find out the curved surface area of a cone, we can multiply the “radius” of the circular base and lateral surface by “pi”. Cone is a three-dimensional figure that has a circular base to a point termed as an apex or a vertex. 

Through the application of the Pythagoras theorem, the relation between the surface area of the cone as well as its height can easily be relatable. The slant height of the cone can easily be calculated by finding out the square root of the summation of the square of the height and the radius of the circular part. 

The formula for curved surface area for cone 

“Curved surface area (CSA) = pi * r *l” 

Where “r”is the radius of the circular base and “l”is regarded as the slant height of the cone 

Properties of a cone 

• Cone has a single base with a single vertex 
• It is a three-dimensional figure 
• It has no edge 
• It depicts two types of areas. One is depicted as a curved surface area and the other is total surface area. 
• The curved surface area can easily be calculated by the multiplication of the base radius, pi, and slant height. 
• It is calculated in square units. 

Examples of the curved surface area of a cone

Find the curved surface area of a cone whose base radius is 10 cm and slant height is 19cm. 

Given: Radius (r) = 10 cm; Slant height (l) = 19cm 

Pi has a constant value of 3.14, 

Curved surface area of a cone = pi * r * l = 3.14* 10* 19 =596.6 square centimeters.

Difference between the total surface area and the curved surface area of a cone 

The total surface area of a cone is regarded as the entire area including both the curved part as well as the base of the cone. Whereas the curved surface area of a cone is regarded as the area of the curved path excluding the base of the circular part. The curved surface area of a cone is also termed the lateral surface area of the cone. For calculating the curved surface area as well as the total surface area of the cone, the figure is usually divided into a circular base and the top slanted part. 

Determinants required to find out the curved surface area of a cone

For determining the curved surface area of a cone, one has to find out the radius of the base of the circular part, the slant height of the cone, and the value of pi. The slant height of the cone can be determined by applying the Pythagoras theorem. 

“The lateral surface area of a cone (l) = √(h2 + r2)” 

The curved surface area of the cone can be determined after finding out the slant height of the cone and the radius of the circular part. 

Characteristics of a cone shape 

A cone is a geometric shape usually 3-dimensional in structure. The figure has a circular base that narrows up to a point at the other end. The figure has a length, width, and respective height. A cone has only a single face or a flat side also termed as the base. The face is circular in shape and the sides of the cone are generally curved and they roll up to a particular point known as apex and vertex. The width of the cone is regarded as the distance across the circular base. It is termed width. The height of the cone is determined as the distance that is from the base to the vertex. There are generally two types of cones in mathematics such as the right circular cone and the oblique cone. 

Difference between a right circular cone and a cone   

A right circular cone is a typical type of cone in which the height is exactly perpendicular to the radius of the circle whereas the cone is a three-dimensional figure with one surface curve and a circular base.

Conclusion

The overall study is based on the curved surface area of a cone and its related formula and its determinants. A cone has a curved surface and a pointed vertex. There are two different types of the surface area of a cone termed total surface area and the curved surface area. Properties of a cone and the formulas that are used in order to calculate the curved surface area of the cone. It can be measured by square units.