A sphere is a three-dimensional round-shaped object. Unlike other three-dimensional shapes, a sphere does not have any vertices or edges. All the points on the surface of the sphere are equidistant from its center. In other words, the distance from the center of the sphere to any point on the surface of the sphere is equal. There are many real-world objects that we see around us which are spherical in shape. Since a sphere is a three-dimensional shape it also has a volume and a surface area. Our planet Earth is not in a perfect shape of a sphere, but it is called a spheroid. The reason it is called a spheroid is it is almost similar to that of a sphere.
|3.||Properties of Sphere|
|4.||Difference Between Circle and Sphere|
|5.||Surface Area of Sphere|
|6.||Volume of a Sphere|
|9.||FAQs on Sphere|
In geometry, a sphere is a three-dimensional solid figure, which is round in shape. From a mathematical perspective, a sphere is a set of points connected with one common point at equal distances. Some examples of a sphere include a football, a soap bubble. The important elements of a sphere are as follows.
- Radius: The length of the line segment drawn between the center of the sphere to any point on its surface. If 'O' is the center of the sphere and A is any point on its surface, then the distance OA is its radius.
- Diameter: The length of the line segment from one point on the surface of the sphere to the other point which is directly opposite, passing through the center of the sphere is called its diameter. The length of the diameter is exactly half of the length of the radius of the sphere.
- Circumference: The length or the distance around the boundary or the outer surface of the sphere is called its circumference.
- Volume: Like any other three-dimensional object a sphere also occupies some amount of space. This amount of space occupied by the sphere is called its volume. It is expressed in cubic units.
- Surface Area: The area occupied by the surface of the sphere is its surface area. It is measured in square units.
As we discussed in the previous section, a sphere has a radius, diameter, circumference, surface area, and volume. Considering a sphere to have a radius of 'r', the following table lists the important formulas of a sphere.
|Diameter||2 × radius of the sphere|
|Circumference||2πr, where π is a constant, which takes the value of 22/7 or 3.14 (approx)|
|Surface Area||4π r2|
Properties of a Sphere
A sphere is a three-dimensional object that has all the points on its outer surface to be equidistant from the center. The following properties of a sphere help to identify a sphere easily. They are as follows:
- A sphere is symmetrical from all directions.
- A sphere has only a curved surface area.
- A sphere has no edges or vertices.
- All the surface points of the sphere are at an equal distance from the center.
- A sphere is not a polyhedron because it does not have vertices, edges, and flat faces. A polyhedron is an object that should definitely have flat faces.
- Air bubbles take up the shape of a sphere because the sphere's surface area is the least.
- Among all the shapes with the same surface area, the sphere would have the largest volume. Sphere volume formula is 4/3 × πr3
Difference Between Circle and Sphere
A circle and a sphere are two different shapes. The important differences between a circle and a sphere are as follows:
|A circle is a two-dimensional shape.||A sphere is a three-dimensional shape.|
|A circle extends in two directions, which are the x-axis and y-axis.||A sphere extends in three directions, which are the x-axis, y-axis, and z-axis.|
|A circle does not have volume.||A sphere has volume since it occupies some space.|
|A circle has one flat face.||A sphere has no faces and one curved surface.|
|The area of a circle is πr2||The surface area of a sphere is 4πr2.|
Surface Area of Sphere
The area covered by the outer surface of the sphere is known as the surface area of a sphere. The surface area of a sphere is the total area of the faces surrounding it. The surface area of a sphere is given in square units. Hence, the formula to find the surface area of a sphere is:
Surface Area of Sphere, S = 4πr2
In terms of diameter, the surface area of a sphere is given as S = 4π(d/2)2, where d is the diameter of the sphere. Check out the surface area of the sphere section for more details
Volume of a Sphere
The volume of a sphere is the measure of space that can be occupied by a sphere. We can determine the volume of a sphere if a string runs along the diameter of a circular disc and when rotated along that string. The unit of volume of a sphere is given as the (unit)3. There are two kinds of spheres - solid sphere and hollow sphere. The volume for both these is different. Hence,
Volume of Sphere, V = (4/3)πr3
- V is the volume,
- r is the radius, and
- π(pi) is approx. 3.412
For more details, check out this section on volume of sphere.
The surface area of a sphere is 4πr2.
The volume of the sphere is 4/3πr3.
In geometry, half of a sphere is known as a "hemisphere".
The total surface area and the volume of a hemisphere formula are exactly half of the sphere area and sphere volume.
Topics Related to Sphere
Check out some interesting articles related to the sphere. Click to know more!
Solved Examples on Sphere
Example 1: Find the diameter and circumference of a sphere with a radius of 7 units.
Given, the radius of the sphere = 7 units.
The diameter of a sphere = 2 × radius.
Therefore diameter of the sphere = 2 × 7
= 14 units.
Circumference of the sphere = 2πr
= 2 × (22/7) × 7
= 44 units
Therefore, the diameter and the circumference of the given sphere are 14 units and 44 units respectively.
Example 2: Find the volume of a sphere whose radius is 8 units.
The formula for the volume of a sphere is (4/3) πr3 cubic units. Take the value of π as 22/7. Given, the radius of the sphere = 8 units. Substituting the value of radius in the formula, we get,
Volume = (4/3) π × 83
= (4/3) × (22/7) × 8 × 8 × 8
= 2145.52 cubic units.
Therefore, the volume of the sphere = 2145.52 cubic units.
Example 3: Find the surface area of a sphere whose radius is 5 units. Take the value of π as 22/7.
Given, the radius of the sphere = 4πr2 square units. Substituting the value of radius in the formula, we get,
Surface Area = 4 × (22/7) × 52
= 4 × (22/7) × 25
= 314.28 square units
Therefore, the surface area of the given sphere is 314.28 square units.
FAQs on Sphere
What is a Sphere?
A sphere is a three-dimensional object with no vertices and edges. All the points on the surface of the sphere are equidistant from its center. Some real-world examples of a sphere include a football, a basketball, the model of a globe. Since a sphere is a three-dimensional object it has a surface area and volume.
What is the Diameter of a Sphere?
The distance of a line segment that connects two opposite points on the surface of the sphere passing through its center is called the diameter of a sphere. The diameter of a sphere is two times its radius.
How is the Surface Area of a Sphere Calculated?
The surface area of a sphere is the area occupied by the surface of the sphere. In simple words, the amount of material used to cover the outer part of a sphere gives its surface area. The formula to find the surface area of a sphere is 4πr2.
How Do You Measure the Volume of a Sphere?
The volume of a sphere is the amount of space occupied by the sphere. For example, imagine a spherical balloon. The amount of air inside the balloon is its volume. The formula for the volume of a sphere is (4/3) πr3.
Does a Sphere Have a Face?
A face is referred to as a flat or curved surface on a three-dimensional object. For instance, a cube has 6 faces. Thereby, a sphere has only one face which is a curved surface. It does not have any flat faces.
What is the Difference Between a Circle and Sphere?
A circle and a sphere are different objects. Since both of them are circular in shape, it creates a notion as if the two shapes are similar. The differences that outline that both are different objects are as follows.
- A circle is a two-dimensional figure whereas a sphere is a three-dimensional object.
- A circle is extended in the x-axis and the y-axis whereas a sphere is extended in three directions (x-axis, y-axis, and z-axis).
- A circle has a surface area only but a sphere has surface area and volume.
Is Sphere Three-Dimensional?
Yes, a sphere is a three-dimensional object that occupies three axes, which are the x-axis, y-axis, and z-axis. It has a surface area and a volume like any other three-dimensional object.
What is the Difference Between a Sphere and a Spheroid?
A sphere is a three-dimensional object that is perfectly spherical in shape. The radius of the sphere is the same at all points of the sphere from its center, whereas, a spheroid resembles a sphere but the radius is not the same at all points from the center of a spheroid. Planet Earth is considered to be a spheroid in nature.