# Sphere Basics

Most three dimensional circular shapes are spherical in structure. These include a globe, a soccer ball, and even an orb.

In the simulation given below, drag the screen and carefully observe the shape of the golden ball through multiple angles.

Isn't it interesting? Let's explore further.

In this lesson, we will explore about Sphere by learning about the definition of the sphere, shape of a sphere, surface area and volume of a sphere, properties of sphere and difference between circle and sphere with the help of interesting simulations, some solved examples and a few interactive questions for you to test your understanding.

## Lesson Plan

 1 What is the Shape of a Sphere? 2 Important Notes on Sphere 3 Solved Examples on Sphere 4 Challenging Questions on Sphere 5 Interactive Questions on Sphere

## Shape of Sphere

### Definition

A sphere, in geometry, is a three-dimensional figure that is perfectly symmetrical and round in shape like a ball or a globe. The word 'Sphere' is taken from the Greek word 'sphaira' which means a ball or a globe.

Any point on the surface of the sphere is equidistant from the center of the sphere. We can say that Circle, in a three-dimensional space, takes the form of a sphere.

## Surface Area of a Sphere

The surface area of a sphere is the area covered by the outer surface of the sphere. The surface area of a sphere is always measured in square units.

A sphere has just one surface only and that too curved.

Therefore, the curved surface area of a sphere is the same as the total surface area of the sphere.

Curved surface area of sphere = Total surface area of a sphere

Let us directly see the formula to determine the surface area of a sphere with radius $$r$$

 Surface Area of a Sphere = $$4\pi r^2$$

Another formula to determine the surface area of sphere using diameter $$d$$ is:

 Surface Area = $$4\pi\left( \dfrac{d}{2} \right)^2$$

Try your hands at the surface area of the sphere calculator and find the area by writing the value of radius.

## The Volume of a Sphere

The volume of a sphere is the capacity that it can hold or the space it occupies. For example, if you blow a balloon, you will see that you can fill air up to a level only and after that, your balloon will burst. So, that is the volume of your spherical balloon.

It is interesting to note that the sphere is the 3D figure that has the smallest surface area for a volume. It means that for the same volume, a cube or any other 3D object will occupy more surface area than a sphere.

The volume of a sphere is always measured in cubic units.

Now let us look at the formula to calculate the volume of a sphere:

 Volume of a Sphere = \begin{align}\frac{4}{3}\pi r^3\end{align}

In the simulation given below, write the value of radius to find the volume of the sphere.

## Properties of a Sphere

Let us look at some properties of the sphere that help us to identify spherical objects from other geometrical figures.

• A sphere has no edges, no faces, and no vertices.
• It has only one curved surface.
• It is not a polyhedron as it does not have a flat face.
• Any point on the surface of the sphere is equidistant from the center of the sphere.
• It is symmetrical in shape as we get two identical halves if we cut it through its diameter. We call it the Hemisphere.

## Difference between Circle and Sphere

If you have a spherical ball that you cut into two pieces, what would be the shape of the cross-section?

You will get a circle, right

Try your hands at the simulation given below and carefully observe the shape of the cross-section of the sphere.

If we cut a sphere through a plane, we get one flat face that is circular in shape.

Thus we can say that a sphere lies in a three-dimensional space and a circle lies on a two-dimensional plane.

The difference between a sphere and a circle is tabulated below:

 Basis of Differentiation Circle Sphere Dimension A circle is a two-dimensional figure. A sphere is a three-dimensional figure. Volume It does not have volume. It has a volume that can be calculated with the help of radius. Faces It has one flat face. It has no faces, as it is not flat. Area Formula Area of a Circle= $$\pi r^2$$ Surface Area of a Sphere= $$4\pi r^2$$
Mensuration and Solids
Mensuration and Solids
grade 10 | Questions Set 1
Mensuration and Solids