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In geometry, a hemisphere is a three-dimensional solid figure that is exactly half the size of a sphere in terms of volume. According to this definition, if a circle is divided into two equal parts, we will get two hemispheres due to the division. You can compare this three-dimensional figure to any half-spherical substance, such as a half lemon and others that are generally spherical. The hemisphere has two surfaces, one curved and the other flat. The flat surface has a circular shape and can be referred to as the circular foundation. This article will cover a wide range of aspects of the hemisphere, including the definition of hemispheres, properties of hemispheres, their characteristics, and other related aspects.
Definition of Hemispheres
The term ‘hemisphere’ provides its meaning; it can be broken down into hemi and sphere, which means half and 3D shape in maths. Hemispheres are 3D shapes that are half of the spheres, with one side flat and the other round. The exact centre of the circle is cut into two halves. The side of the hemisphere that is flat is called the base or the face of the hemisphere. The word hemisphere is derived from the prefix of the word ‘sphere,’ which means ‘perfectly circular,’ in Greek. Because it is an exact half of a sphere, it is called a hemisphere.
Properties of Hemispheres
A hemisphere is a three-dimensional geometric figure half the size of a sphere. It has flat and curved surfaces on both the inside and outside. Consequently, it is the exact half of a sphere in shape. Two halves make up a sphere.
There is only one curved edge on a hemisphere where the curved face meets the flat face.
You can find out how big each hemisphere is by looking at the lines that meet at its centre and opposite ends on its base. This is called its diameter.
The hemisphere is not a polyhedron because polyhedrons are made up of polygons. A hemisphere has a more circular base and curved surface than a polyhedron.
It is possible to define the diameter of a hemisphere as a line segment that passes through its centre and touches two points on its base opposite one another.
The radius of a hemisphere is defined as a line segment connecting the centre of the hemisphere to a point on its curved surface.
Volume of a hemisphere
The volume of a hemisphere is equal to the total capacity of the hemisphere multiplied by the number of unit cubes that can be accommodated within that area. It is possible to measure the volume of a hemisphere in cubic units, denoted by the letters m3, cm3, in3, etc.
The formula to find the Volume of the Hemisphere is
= (2πr*r*r)/3,
Wherein the term π represents or is the constant equal to 22/7, and the term r represents the radius of the Hemisphere.
Surface area of a hemisphere
The surface area of a hemisphere can be found by multiplying the area of its base with the area of its curved surface, which is a circle.
Hollow or solid: The surface area can be found based on the Hemisphere’s appearance, which can be hollow or solid. Square units are used to measure it.
The formula to find the hemisphere’s surface area is
= 3πr*r,
wherein the term π represents or is the constant which is 22/7 and the term r represents the radius of the Hemisphere.
Types of hemispheres
There are only two types of hemispheres: 1. Solid Hemispheres 2. Hollow Hemispheres
Solid Hemispheres: These are three-dimensional objects with the shape of the exact half of a sphere and are filled with the same material they are made of. It’s also called a solid sphere.
Hollow Hemispheres: A two-dimensional object is called a hollow hemisphere, and only its outer circular bowl boundary defines it. It doesn’t have any substance inside of it.
Key differences between a hemisphere and a sphere:
A sphere can be used to make a hemisphere, and the two objects have many similarities and some differences. Spheres and hemispheres differ in the following ways.
Hemisphere | Sphere |
A three-dimensional representation of a sphere cut in half | 3D figure with no edges or vertices |
One side is flat and the other is curved | Only curved, no flat sides |
The volume of a hemisphere = (2/3)πr3 cubic units | The volume of a sphere = (4/3)πr3 cubic units |
Contains total surface area and lateral surface area | The surface area of a sphere is 4πr2 |
Conclusion
Hemispheres are some of the most common and prominent shapes. They have characteristics similar to those of spheres but distinct enough to be relevant in geometry. This article discussed the properties and aspects of the hemisphere.
