In Mathematics, there are many geometrical shapes. Any materialist entity in the whole universe can be present in the form of geometrical shapes. For many mathematical shapes, there exists a relationship between them. Let us start with a simple example. We know that there is a relationship between lines and shapes. A line is formed by joining many points or dots in the plane surface. Similarly, a shape is defined by the combination of many lines. Several lines can create shapes. If a shape has three lines, it is known as a triangle. If the shape has four lines, then it is either a square, rectangle, rhombus, and so on. Here, let’s discuss the relationship between the sphere and various geometrical shapes.
We know that a sphere and a cylinder are three-dimensional shapes. A sphere is a collection of points, in which all points lie on the surface having the same distance from the centre point called radius. A cylinder is a closed solid object with two parallel bases and curved surface. There exists a relation between these two shapes such that the sphere volume is two-thirds of the volume of the cylinder, if they have the same radius and cylinder height is equal to the sphere diameter.
Similarly, the relationship between the sphere and the cone is established by means of the volume of the cylinder. A cone is a solid, hollow object that tapers smoothly from the flat circular base to the point called apex. We know that the volume of the cone is one-third of the volume of the cylinder. Now, by means of a cylinder, as discussed above, there exists a relation between the sphere and cone. Likewise, there is a relationship between the sphere and hemisphere. It means that the sphere volume is equal to two times the volume of a hemisphere. Since a hemisphere is half of the sphere, the surface area of the hemisphere is also determined from the surface area of the sphere.
In the real world, many geometrical shapes are analyzed using many statistical methods. Statistics is a branch of Mathematics, which is classified into two different types, namely descriptive statistics and inferential statistics or statistical inference. For instance, to quantify the difference between the male and the female skull, a statistical shape analysis process is used. This process helps to analyze the geometric properties of any shape. Learn more interesting facts about many geometrical shapes by subscribing BYJU’S YouTube channel and explore more videos.