A sphere is a round-shaped three-dimensional figure that is defined in three axes, namely, x-axis, y-axis, and z-axis. Through this article one can learn the meaning, elements, properties, surface area formula, and volume of sphere formula.
In mathematics, a sphere is a three-dimensional geometrical round-shaped figure. In other words, the sphere can be defined as the set of points connected with one common point at equal distances. Some real-life examples of spheres include football, a soap bubble, basketball, world globe, planets, marbles, and many others.
Below-given are some major elements of a sphere:
- Radius: The length of a line segment connecting the center and any point on the surface of the sphere is called a radius.
- Diameter: The length of a line segment passing through the center connecting one point on the surface of the sphere to another point on its surface is called the diameter. The length of the diameter is exactly double the length of the radius of the sphere.
- Circumference: The distance around the boundary or length of the boundary is known as the circumference of the sphere.
- Volume: Sphere like any other three-dimensional geometrical figure occupies some amount of space. The region occupied by the sphere is called its volume and is expressed in cubic units.
- Surface Area: The region covered by the surface of the sphere is called it’s surface area and is expressed in square units.
There are some basic properties of the sphere and these properties are also known as the attributes of a sphere.
- The three-dimensional figure of a sphere is symmetrical in all directions.
- The sphere has a curved surface area.
- A sphere is not considered a polyhedron because there are no vertices, edges, and flat faces.
- All points on the boundary of a sphere are equidistant from its center.
- The width and circumference of a sphere are constant.
- A sphere does not have a surface of centers.
- The volume of a sphere is the largest compared to the shapes having the same surface area as a sphere.
The surface area of a sphere:
The area that is covered by the outer surface of a sphere is defined as the surface area of a sphere. Its surface area is given by square units. The mathematical formula to calculate the surface area of a sphere is as follows:
Surface Area of Sphere = 4πr2 Square units
In case if the diameter of a sphere is given instead of the radius, then the formula to calculate the surface area of a sphere is:
Surface Area of Sphere = 4π(d/2)2 Square units
The volume of a sphere:
The volume of a sphere is defined as the space occupied by the sphere. The volume of the sphere can be determined with a string running along the diameter of a circular disc and when rotated along that string. The measurement unit of the volume is given as (unit)3. Two types of spheres can be found- solid sphere and hollow sphere. The mathematical formula to calculate the volume of both types of a sphere is:
The volume of Solid Sphere = (4/3)πr3
The volume of Hollow Sphere = Volume of Outer Sphere – Volume of Inner Sphere
= (4/3)πR3 – (4/3)πr3 = (4/3)π(R3 – r3)
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