Cone-Total Surface Area

The surface area of an object can be introduced as the area covered by the surface of that object. Cone is a three-dimensional shape that narrows from the base towards the apex. Surface area is a two-dimensional quantity. Cone has a circular base at the bottom and vertex at the top. The flat surface of the cone is known as the base of the cone. 

 Discussion

3.1 Total Surface Area of Cone

Surface area is the summation of all the surfaces of a given three-dimensional object. It can be measured by the multiplication of length and width. Cone has basically two surfaces. The first one is at the bottom, which is known as a circular base. The second one is the outside surface above the circular base. The surface area of the cone can be measured by the summation of these two surfaces of the cone. Several items in real life can be examples of cones such as Christmas tree, carrot, ice-cream cone, party hat, etc. From one side a cone can be seen as a triangle. From the top view, the cone seemed like a point, and from the bottom view, it seemed like a circular plate. 

3.2 What is the total surface area of the cone?

Surface area can be measured in square units because only length and height are to be used to determine the surface area of an object. There are two types of surface area Total surface area and Curved surface area or Lateral surface area. Total surface area is the combination of the surface area of the base and the curved surface area. It is the total area that is covered by all the surfaces of the object. If an object has a curved surface and plane surface then to determine the total surface these two surface areas have to be combined. On the other hand, the curved surface area is known as only the surface area that is covered by the curved surface of the object. The curved surface area also can be called the lateral surface area for objects like the cylinder. There are several differences between the volume and surface area. Volume is a three-dimensional quantity. For determining the volume of an object length, breadth and height must be required. There are several kinds of geometric shapes in mathematics such as rectangle, triangle, square, parallelogram, trapezoid, circle, etc. 

3.3 Total surface area of cone formula

The surface area of a cone can be determined from the given formula:

“A=πr(r+√ (h2+r2))”

In this formula A denotes the surface area of the cone, r is the radius of the circle that is situated at the bottom of the cone and h is the height of the cone. Here π is the ratio of 22 and 7. 

In this formula, “√(h2+r2)” denotes the slant height of the cone. The slant height of a cone can be denoted as l. In this way, the formula of the surface area of the cone can be expressed in a different way like:

“A=πr(r+l)”

In this equation, l is equal to √(h2+r2). From the Pythagorean Theorem, it can be described easily. According to this theorem, the hypotenuse of a right-angled triangle is the summation of individual square roots of height and base. It can be expressed easily with the formula:

“C=√(A2+B2)”

Here, the hypotenuse of the right-angled triangle is denoted by C . “A” and “B” are the base and height of the right-angled triangle respectively. 

The surface area formula of the cone, the term “πr2” denotes the area of the circular base of the cone. It is also called the plane surface area. On the other hand, the curved surface area of the cone can be determined by the given formula:

“S=πrl”

Here S denotes the curved surface of the cone and π, r and l denote the ratio of 22 and 7, the radius of the circular base of the cone, and slant height of the cone respectively. 

Cone is a type of three-dimensional geometric shape that can be rotated about its vertex. For painting a conical flash the surface area of that conical flask should be determined before painting. It also should be determined that for the painting of one square how much quantity of paint should be required. Then the total surface area and quantity of paint per square unit should be multiplied. The final result after multiplication is the quantity of the paint that should be required for the painting of the conical flask. 

Conclusion

The surface areas of several geometrical objects are different. Basically, length and width are used to determine the surface areas of several objects. For circular, only diameter or radius is used for the determination of surface area. The surface area of the cone is determined to paint the surface of any object that is shaped like a cone. Also, the surface area of a floor can be determined to calculate how many plates are required to finish the floor. Cone is a three-dimensional geometric shape.