What is Sphere Shape?
In Geometry, a sphere is characterized as a set of all points in a three-dimensional space lying on the same distance (known as the radius) from a fixed point (known as the centre) or the result of turning a circle about one of its diameter. A sphere has no edges or vertices. It is perfectly symmetrical. The components and properties of sphere shape are similar to those of a circle. A sphere with radius ‘r’ has a volume of \[\frac{4}{3}\] πr³ or surface area of 4πr².
(Image will be uploaded soon)
Example of Sphere Shapes
Following are the different examples of sphere shapes:
(Image will be uploaded soon)
Important Terms of Sphere Shape
Some important terms of sphere shape are as follows:
Radius
The distance from the fixed point that is the centre of the sphere to any point on its surface is termed as the radius of a sphere.
(Image will be uploaded soon)
Diameter
The diameter of a sphere is the longest straight line through a sphere joining two points of a sphere and passing through its fixed center point. The length of the diameter of a sphere is twice the length of its radius.
(Image will be uploaded soon)
Circumference
The circumference of a sphere is the distance around the boundary or the outer surface of the sphere.
(Image will be uploaded son)
Meridian
The meridian is any great circle of the celestial sphere that passes through its poles that are north and south celestial poles and an observer’s zenith.
The top part of the meridian is the semicircle above the observer’s horizon whereas the bottom part of the meridian is the semicircle below the observer’s horizon.
(Image will be uploaded soon)
Geodesic
The Geodesic is the intersection of the sphere with a plane through its centre joining two points on its surface. In short, on the sphere, Geodesics are a great circle (like an equator).
(Image will be uploaded soon)
Great Circle
A great circle, also termed as orthodrome, is a circle drawn on the surface of a sphere by the intersection of a plane that passes through the centre of a sphere. A great circle divides the circle into two halves known as the hemisphere. The great circle of a sphere, also known as the Romanian Circle, forms as the base of the sphere which is a flat side.
(Image will be uploaded soon)
What is a Hemisphere?
Hemisphere is a name assigned to the half sphere.
Hemisphere is most commonly used when describing the different areas of the Earth.
Any circle drawn around the Earth splits into two different halves, known as hemispheres.
Spherical Shapes Formula
Here, we will learn to calculate the volume, circumference, diameter and surface area of a spherical shape.
Volume of Sphere
The amount of space occupied by the solid sphere is termed as the volume of the sphere.
Volume of Sphere Formula : \[\frac{4}{3}\] πr³
Here, the value of π is 3.14.
‘r’ is the radius of a sphere.
The most commonly used cubic units of a sphere shape are m³, cm³, inch³ and ft³.
Surface Area of Sphere
The surface area of the sphere is four times the area of a large cross-sectional circle, called the great circle.
Surface Area of Sphere Formula : 4πr² or πd²
Here, the value of π is 3.14.
‘r’ is the radius of a sphere.
‘d’ is the diameter of a sphere.
Circumference of Sphere
The circumference of a sphere is the distance covered around the sphere. The unit of circumference of the sphere is the same as radius. The circumference of sphere can be calculated by using the following formula:
Circumference of sphere: 2πr
Here, the value of π is 3.14.
‘r’ is the radius of a sphere.
Diameter of Sphere
The diameter of a sphere is defined as the line passing through the centre from one end to the other end. The formula to calculate the diameter of a sphere is given below:
Diameter of sphere: 2 × r
‘r’ is the radius of a sphere.
Sphere and Circle Difference
Following is the key difference between sphere and circle:
A sphere in geometry is a three-dimensional solid object while a circle in geometry is a two-dimensional object.
We can find surface area of circular shaped objects whereas in spherical shaped objects, we can also find volume along with surface area. In other words, a circular shape object does not have volume whereas a spherical shape object has volume
Solved Examples
1. Calculate the volume of a spherical shape object with radius 3 cm?
Solution:
As we know, the volume of a sphere formula is \[\frac{4}{3}\] πr³.
Accordingly, the volume of a spherical shape object with a given radius 3 cm is
\[\frac{4}{3}\] πr³ = \[\frac{4}{3}\] π × \[\left ( 3 \right )^{3}\] = \[\frac{4}{3}\] π × 27 = 36π
Substituting the value of π, we get 36 × 3.14 = 113.04
Hence, the volume of sphere with radius 3 is 36 or 113.04 cm³.
2. Calculate the surface area of a spherical shape object with radius 14 cm?
Solution:
As we know, the surface area of a sphere formula is 4πr².
Accordingly, the surface of a sphere with radius 14 is
4πr² = 4π × \[\left ( 14 \right )^{2}\] = 4π × 196 = 784π.
Substituting the value of π, we get 784 × 3.14 = 113.04.
Hence, the volume of sphere with radius 14 is 784π or 2,461.76 cm².
FAQs on Sphere Shape
1. How many surfaces does the sphere have?
A sphere has only one continuous surface. Perfect sphere has a smooth surface where every point is the same distance from the centre. The spherical shape in real life can be rough or bumpy.
2. What are the properties of a sphere?
The different properties of sphere are as follows:
The spherical shape objects are perfectly symmetrical around its centre.
It has no edges or vertices.
It is not a polyhedron.
It has only one surface
3. What is the shape of a sphere?
The shape of a sphere is circular in shape and it does not have any faces. A sphere is a three-dimensional object having curved surfaces. Like any other solid object such as cube, cubic, cone and cylinder, a sphere does not have any flat surface or vertex or edge.
