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How Would You Define the Surface Area of Cone?

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You must be knowing about figure Cone. It’s a three-dimensional figure. As the term suggests surface area of cone, this literally means the whole or the total surface area which is being covered by the base area and the lateral surface area of the cone. A Cone is such a geometrical figure which is defined to have a 3D structure with a circular base. This structure can be alternatively viewed as a set of congruent circular disks which is being placed on top of one another in a way that the ratio of the radius of the disks which are adjacent to each other remains constant always. 

Different Formula for Different Sections of The Cone

The surface area of a cone is a whole complete area that is being covered by two of its surface area, that is the lateral or the curved portion of the figure. The surface area of the cone has a different formula to calculate, while the circular base of the cone can be estimated using the area of the circle formula. In the next section, we will illustrate the formula of the surface area of a cone. 

The Formula for The Surface Area of a Cone   

As discussed already, the surface area of the cone is the total area that is being occupied by its surface in the form of the three-dimensional plane structure. The formula of the surface area of the cone will contain the sum of its curved surface area and the circular base area of the cone. 

The Formula:   

Surface Area of a Cone = πr(r+√(h2+r2))

In this formula, r is the radius of the circular base, h is the height of the cone.

What Will Be the Surface Area of Sphere? 

The surface area of the sphere is simply the area that is being occupied by the total surface structure of the geometric figure – sphere. The circular shapes for the sphere are for the three-dimensional figure. In real life, the globe or the football ball will have this structure.  Also, this is to be noted that a circle is a 2-D structure while a sphere is a 3-D structure. The surface area of the sphere is the total surface area having the faces which surround it. The measurement of the surface area of the sphere is to be calculated in square units.  


What Will Be the Formula to Calculate the Surface Area of Sphere?

The formula which is required for calculating the surface area of the square will depend upon the radius of the sphere. Suppose ‘r’ is the radius of the sphere and ‘S’ is the surface area of the sphere. So, the formula for the surface area of the sphere will be – S= 4πr2. While, in terms of the diameter of the sphere this is to be given as S = 4π(d/2)2, ‘d’ being the diameter of the sphere. 

How Can You Calculate the Surface Area of Sphere?

The surface area of the sphere is the space that is occupied inside the part of the square. The steps are given as under to find out the surface area of the sphere. The steps are as follows: 

  • Step 1: First know the radius of the sphere.
  • Step 2: Now square up the radius and then multiply with itself. 
  • Step 3: Next, you need to multiply r2 by 4.
  • Step 4: The value of 4r2 is to be multiplied with an approximate value of the pi which is 3.14
  • Step 5: Now add up the units to find the final answer. 

This is how you need to calculate the surface area of the sphere. 

In this context, we have learned about the surface area of the cone and sphere. Students are required to practice the sums using the formula of the total surface area of the cone and sphere. If you aspire to know more related to this content or any other mathematical content, feel free to access the Cuemath website. They offer a range of interesting concepts which will clarify doubts of the young maths learner.