# Volume of Hemisphere: Formula and Solved Examples

In geometry, we learn about different dimensional shapes: One-dimensional, two-dimensional and three-dimensional shapes. Three-dimensional shapes have three measurements: length, breadth, and height. The volume of an object refers to the space occupied by three-dimensional objects. In this section, we will cover the volume of a hemisphere with some solved examples.

## What is a Hemisphere?

A sphere is a three-dimensional shape with each point on its surface equidistant from the centre. The term ‘Hemi’ means half as it is denoted by the half of the sphere. A hemisphere is formed when a plane divides a sphere into two equal parts from its centre. So a hemisphere is half of a sphere. Basically, a hemisphere is a three-dimensional object that is flat from one side and has a bowl-like shape on the other side.  For example, the earth is a single big sphere divided into two hemispheres: northern and southern.

## What are the properties of the Hemisphere?

The hemispheres have the following properties:

• A hemisphere has no edges and vertices.
• A hemisphere has one curved surface and one flat surface.
• A line segment that connects two opposite points on the circumference of the circle and passes through its centre is called the diameter of the hemisphere.
• A line segment from the centre to any of the points on the circumference of the circle is the radius of the hemisphere.

## What is the Volume of the Hemisphere?

The volume of a hemisphere refers to the space occupied by a hemispherical object. Any object with a large volume takes up a large space. The volume of a hemisphere can also be described as half the volume of a sphere. The formula is calculated by Archimedes.

Also Read: Difference Between Volume and Area

## Formula of Volume of Hemisphere

The formula for the volume of a hemisphere is 2πr3/3 cubic units.

Where, π = 3.14

Now, let’s look at how the formula is derived.

The volume of a sphere= 4πr3/3

As the hemisphere is the half of the sphere, the volume will be;

= 1/2 x  4πr3/3

=2πr3/3

## How to Find the Volume of a Hemisphere

The volume of the hemisphere can be calculated by using the formula, which is 2πr3/3. So, let’s follow the steps to find the volume of the hemisphere if the radius is 3 cm.

Step 1: The radius of a hemisphere is 3 cm, which can be denoted as ‘r’.

Step 2: Substitute the value of the radius in the formula2πr3/3 and write the value of π as 3.14.

Step 3: Now calculate the value by 2 x 3.14 x 3x3x3/3 = 56.52 cubic units.

Also Read: Difference Between Power and Exponent

## Solved Examples

1. Find the volume of a hemisphere with a radius of 3 cm.

The volume of the hemisphere= 2πr3/3

= 2x 3.14 x (3)3/3

= 6.28 x 27/3

= 6.28 x 9

= 56.52 cubic units

1. Find the volume of the hemisphere with a diameter of 12 cm.

Diameter of hemisphere= 12 cm

= 6 cm

The volume of the hemisphere= 2πr3/3

= 2x 3.14 x (6)3/3

= 6.28 x 216/3

= 6.28 x 72

= 452.16 cubic units

## FAQs

What is a hemisphere?

A hemisphere is formed when a plane divides a sphere into two equal parts from its centre. So a hemisphere is half of a sphere. For example, the earth is a sphere divided into two hemispheres: northern and southern.

What is the volume of a hemisphere?

The volume of a hemisphere refers to the space occupied by a hemispherical object. Any object with a large volume takes up a large space. The volume of a hemisphere can also be described as half the volume of a sphere. This formula is calculated by Archimedes.

What is the formula for the volume of the hemisphere?

The volume of the hemisphere= 2πr3/3 cubic units.
Where, π = 3.14