Sphere-Surface Area

Introduction

Sphere is a subject associated with mathematics. Sphere is a “three-dimensional” structure having a circular shape. The “area of a sphere” can be explained as the neighbourhood outlined by the sphere is known as the “surface area of sphere”. One thing that differentiates a circle and a sphere is that a circle has a “two-dimensional” structure whereas a sphere has a “three-dimensional” structure. Circle has a flat shape whereas the circle does not.

Surface Area of Sphere

Surface area of a sphere can be defined as the whole region that covers the outer surface of a whole sphere. This has also been seen to be measured in three-dimensional space. A sphere can thus be represented as a round-shaped three dimensional solid. Though a sphere can be represented as a circle, there has been a key difference between a sphere and a circle. This key difference has been seen to be that a circle can be described in a two-dimensional space and a sphere can only be described in a three-dimensional space. 

A sphere can be constructed by rotating a circular disc with one of its diagonals being fixed. The surface area of a sphere can be classified into three major types and these types are Lateral surface area, Curved surface area and Total surface area. Lateral surface area can be represented as all areas of regions of a sphere except its base. Curved surface area can be defined by adding area of all curved regions of a sphere and Total surface area can be defined as the area of all sides of a sphere from top to bottom.

What is the Surface Area of a Sphere

The surface area of a sphere can be defined as are which can be occupied by a curved surface of a sphere. A circle can be represented as a sphere when it has been represented in a three-dimensional space. As an example, a soccer ball can be taken as a sphere as it is circular and can only be represented in a three-dimensional space. Thus it can be said that a sphere is nothing but a circle that has been represented in a three-dimensional space. The surface area of a sphere has been seen to be expressed in units of squares. As a sphere is generally round in shape, thus to find its surface area, it can be represented as a cylinder having a curved surface. Now, if the radius of a sphere is equal to the radius of a cylinder, it defines that respective sphere can fit into that cylinder perfectly. This can also define that the height of both cylinder and sphere is same. If the height of both solids is the same, then that height can define the diameter of that sphere. Archimedes depicted that if the radius of the sphere and cylinder is represented by “r”, then the surface area of that sphere can be equal to the lateral surface area of that cylinder. Thus the relation between the lateral surface area of a cylinder and the surface area of a sphere can be seen to be equal to each other.

The volume of a circular object which has been enclosed by a sphere of radius R is (4/3)*π*R3 and the formula which can define the surface area of a sphere of radius R is 4*л*R2. From these equations, it can be seen that the surface area of a sphere is derivative of the surface area of a sphere that has been enclosed by a sphere with respect to R.

Surface area of a sphere formula

The “surface area of the sphere” can be expressed as in mathematical form and it can be denoted as “SA = 4𝝅r2”. Where SA is referred to as Surface Area, and “r” is expressed as the radius of the sphere. The surface area of the sphere concept can be understood by a few mathematical examples. Such as:

• Find out the cost required to buy land which is in the form of a sphere and radius is 10 cm. If the buying cost of the land will be INR 1000 sq/cm. (Consider the value of 𝝅 as 22/7).

Solution: From the above question, we know the “area of the sphere is 4𝝅r2”. 

                 r = 10 cm

Therefore, 4𝝅r2 = 4 * (22/7) * 102

                           = 1257.14 cm2

Thus, the total cost for buying the land will be = 1257.14 * 1000 = INR 1257140

• Find out the surface area of a sphere having volume 12 cm3.

Solution: V = (4/3)*𝝅*r2

                 12 = (4/3)*(22/7)*r2

                  r = 1.7 cm

Hence, SA = (4)*(22/7)*(1.7)2

                  = 36.33 cm2

Conclusion

As a mathematical definition, a sphere is associated with geometry, having a three-dimensional structure. A sphere has a 3D structure; it does not have any edges and vertices. The “area of the sphere” was first discovered by the great mathematician Archimedes. The “surface area of the sphere” can also be calculated with the help of calculus. Like a circle, a sphere does not look flat like a circle does.