Table of Contents
Definition of Sphere
Sphere and its properties: A sphere is a three-dimensional shape that has all points on its surface equidistant from a common center. It is a closed surface with no edges.
What is a Sphere?
As discussed in the introduction, the sphere is a geometrical figure that is round in shape. The sphere is defined in a three-dimensional space. The sphere is three dimensional solid, that has surface area and volume. Just like a circle, each point of the sphere is at an equal distance from the center.
| Radius | The distance between surface and center of the sphere is called its radius | ||||||||
| Diameter | The distance from one point to another point on the surface of the sphere, passing through the center, is called its diameter. | ||||||||
| Surface area | The region occupied by the surface of the sphere is called it’s surface area | ||||||||
| Volume | The amount of space occupied by any spherical object is called its volume
Shape of SphereThe shape of a sphere is round and it does not have any faces. The sphere is a geometrical three-dimensional solid having a curved surface. Like other solids, such as cube, cuboid, cone and cylinder, a sphere does not have any flat surface or a vertex or an edge. The real-life examples of the sphere are:
Properties of a sphereThe important properties of the sphere are given below. These properties are also called attributes of the sphere.
Equation of a SphereIn analytical geometry, if “r” is the radius, (x, y, z) is the locus of all points and (x0, y0, z0) is the center of a sphere, then the equation of a sphere is given by:
Sphere FormulasThe common formulas of the sphere are:
Surface Area of a SphereThe surface area of a sphere is the total area covered by the surface of a sphere in a three-dimensional space. The formula of surface are is given by:
Where “r” is the radius of the sphere. Volume of a SphereThe amount of space occupied by the object three-dimensional object called a sphere is known as the vol. |
Properties of Sphere
A sphere is a three-dimensional shape that is defined as the set of all points in three-dimensional space that are equidistant from a given point called the center of the sphere. Here are some properties of a sphere:
1. Surface area: The surface area of a sphere is given by the formula A = 4πr², where r is the radius of the sphere. This formula gives the total area of the surface of the sphere, including the top, bottom, and curved sides.
2. Volume: The volume of a sphere is given by the formula V = (4/3)πr³, where r is the radius of the sphere. This formula gives the total amount of space enclosed by the sphere.
3. Diameter: The diameter of a sphere is the distance between any two points on the sphere that are opposite to each other. It is equal to twice the radius of the sphere.
4. Circumference: The circumference of a sphere is the distance around the equator of the sphere. It is given by the formula C = 2πr.
5. Center: The center of a sphere is the point from which all points on the surface of the sphere are equidistant.
6. Great circle: A great circle is a circle on the surface of the sphere whose center coincides with the center of the sphere. All great circles on a sphere have the same circumference, and they divide the sphere into two equal hemispheres.
7. Meridian: A meridian is a great circle on the surface of the sphere that passes through the poles of the sphere.
8. Latitude and longitude: The coordinates of a point on the surface of the sphere can be specified using latitude and longitude. Latitude is the angle between the point and the equator, measured along a meridian. Longitude is the angle between the point and the Prime Meridian, measured along the equator.
9. Symmetry: A sphere has rotational symmetry around any axis that passes through its center. This means that it looks the same from any direction.
10. Maximum volume: A sphere has the maximum volume among all shapes with a given surface area. This property is known as the isoperimetric inequality.
Infinity Learn App
Now you can find answer to all your subject queries & prepare for your Exams on our Online Learning App – Infinity Learn.
