What Is the Sphere Shape Definition Formula Properties and Examples
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.
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Example of Sphere Shapes
Following are the different examples of sphere shapes:
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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.
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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.
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Circumference
The circumference of a sphere is the distance around the boundary or the outer surface of the sphere.
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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.
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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).
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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.
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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 in Geometry Definition and Formulas
1. What is a sphere in geometry?
A sphere is a three-dimensional shape in which all points on the surface are at an equal distance from a fixed point called the center. This constant distance is known as the radius.
- A sphere has no edges or vertices.
- It is perfectly round in all directions.
- Examples include a ball, globe, and bubbles.
2. What is the formula for the volume of a sphere?
The volume of a sphere is given by the formula V = (4/3)πr³, where r is the radius.
- π ≈ 3.1416
- r = radius of the sphere
V = (4/3) × π × 3³ = (4/3) × π × 27 = 36π cm³ ≈ 113.1 cm³.
3. What is the surface area of a sphere?
The surface area of a sphere is calculated using the formula A = 4πr², where r is the radius.
- This measures the total outer area.
- It depends only on the radius.
A = 4 × π × 25 = 100π cm² ≈ 314.16 cm².
4. What is the difference between a sphere and a circle?
A sphere is a three-dimensional shape, while a circle is a two-dimensional shape.
- A circle lies on a flat plane.
- A sphere has volume and occupies space.
- A circle has area only, but a sphere has both surface area and volume.
5. How do you find the radius of a sphere if the volume is given?
The radius of a sphere can be found from volume using the formula r = ∛(3V / 4π).
- Start with V = (4/3)πr³.
- Rearrange to solve for r.
r³ = (3 × 288π) / (4π) = 216,
r = 6 cm.
6. How many faces, edges, and vertices does a sphere have?
A sphere has 0 faces, 0 edges, and 0 vertices.
- It has one continuous curved surface.
- There are no flat surfaces.
- No corners or line segments exist.
7. What is the diameter of a sphere?
The diameter of a sphere is twice the radius and is given by d = 2r.
- It passes through the center.
- It is the longest distance across the sphere.
8. What are the properties of a sphere?
The main properties of a sphere describe its symmetry and measurements.
- All surface points are equidistant from the center.
- It has rotational symmetry in all directions.
- Surface area = 4πr².
- Volume = (4/3)πr³.
- No edges or vertices.
9. What is a hemisphere?
A hemisphere is half of a sphere formed by cutting it along its diameter.
- Volume = (2/3)πr³
- Curved surface area = 2πr²
- Total surface area = 3πr² (including the flat circular base)
10. Where are spheres used in real life?
A sphere shape is used in many real-life objects because it distributes force evenly and has minimum surface area for a given volume.
- Sports balls (football, basketball).
- Planets and stars in astronomy.
- Bearings in machinery.
- Water droplets and bubbles.
