Area of a Sphere

What is a Sphere?

The word sphere has its origin from the Greek word saphaira, which means a ball or a globe. In simple terms, a sphere is a perfect circle in 3-D space. The only difference between a circle and a sphere is their orientation in the space. A circle is 2D, whereas a sphere is 3D. A sphere is a round-shaped object in three dimensions. A sphere has no vertices or edges, unlike other three-dimensional forms. Equidistant from the center are all points on the spherical surface. In other words, the distance between the center of the sphere and any point on the sphere's surface is equal. We observe several real-world things in spherical form around us. Given the three-dimensionality of a sphere, it also has a surface and volume. Our planet Earth is not a perfect sphere but a spheroid. It's almost comparable to that of a sphere and therefore referred to as a spheroid. The sphere shares the same properties as a circle, like a radius, diameter, chord area, etc. Still, due to 3D orientation, it possesses some distinct features like lateral surface area, curved surface area, and volume.

Properties of a Sphere

The following characteristics aid us to easily identify a spherical object. They are listed below:

• A sphere from all perspectives is balanced or symmetric.
• A sphere has a curved surface area only.
• All of the sphere surface points are equally far from the center.
• An object that certainly has flat faces is a polyhedron. The sphere is not a polyhedron since the vertices, edges, and flat surfaces are not present.
• Air bubbles assume the spherical form since the surface area of the sphere is the least. This is the same reason for all the heavenly bodies to have an almost spherical shape.
• The sphere will have the greatest volume among all forms with the same surface area.

Area and Formula for the Area of a Sphere

• There are three surface areas for any 3D object, namely the Total surface area, Lateral surface area, and curved surface area.
• The region covered by any item having curved surfaces is known as the curved surface area.
• This area is calculated with the help of ‘pi’, which equals 3.14.
• The lateral surface area can be defined as the area of an item without the top and base.
• The total surface area is the area swept by the entire object in the 3D space.
• Since a sphere is deficient in a top and bottom and has absolutely no flat surface, the curved surface area is its total surface area.

The area of a hollow sphere = 4 x pi x r², where r is the internal radius of the sphere. Suppose we substitute the value of r as D/2 (D is the diameter of the sphere), the formula changes and becomes pi x D².

From the equation, it is clear that a sphere’s area is four times to that of a circle with the same radius. The unit of measurement is square units.