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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.
Table of Contents
What is the Volume of Hemisphere?
A sphere is a three-dimensional shape with each point on its surface equidistant from the centre. 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 equal parts known as the northern hemisphere and the southern 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
r= radius of the hemisphere
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
Also Read: Difference Between Power and Exponent
Solved Examples
- 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
- Find the volume of the hemisphere with a diameter of 12 cm.
Diameter of hemisphere= 12 cm
Radius of hemisphere= 12/2 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
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FAQs
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.
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.
The volume of the hemisphere= 2πr3/3 cubic units.
Where, π = 3.14
r= radius of the hemisphere.
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