A hemisphere, in general, refers to half of the earth such as the northern hemisphere or the southern hemisphere. But in geometry, a hemisphere is referred to as a 3D figure made from cutting a sphere into two equal halves with one flat side. In real life we come across various objects that are in the shape of a hemisphere for example if we cut a cherry into half, we get a hemisphere-shaped cherry or if we cut a grapefruit into half we get a hemisphere. Let's learn more about a hemisphere, the definition, its properties, formulas and solve a few examples.
Definition of a Hemisphere
The word hemisphere can be split into hemi and sphere, where hemi means half and sphere is the 3D geometric shape that is used in math. Hence, a hemisphere is a 3D geometric shape that is half of a sphere with one side flat and the other side as a circular bowl. A hemisphere is formed when a sphere is cut at the exact center along its diameter leaving behind two equal hemispheres. The flat side of the hemisphere is known as the base or the face of the hemisphere. Therefore, a hemisphere is considered as an exact half of a sphere.
Properties of a Hemisphere
Since a hemisphere is the exact half of a sphere, they share very similar properties as well. They are as follows:
- A hemisphere has a one curved surface area
- Just like a sphere, there are no edges and no vertices in a hemisphere
- A hemisphere is not a polyhedron since polyhedrons are made up of polygons, but a hemisphere has one circular base and one curved surface.
- The diameter of a hemisphere is a line segment that passes through the center and touches the two opposite points on the surface of the hemisphere
- The radius of a hemisphere is a line segment from the center to a point on the surface of the hemisphere
- The great circle of a sphere forms as the base of the hemisphere which is the flat side. It is created when a plane intersects the center of a sphere cutting it into two equal halves.
Difference Between Hemisphere and Sphere
We already know that a hemisphere is obtained from a sphere and the two objects share very similar properties, but there are a few differences as well. Listed below are the few differences between a sphere and a hemisphere.
|A 3D figure obtained by cutting a sphere in half||
A 3D figure used in geometry that has no edges and no vertices.
|Has one flat side and one curved side||Has no flat side and is only curved|
|The volume of a hemisphere = (2/3)πr3||The volume of a sphere = (4/3)πr3|
Hemisphere has two surface areas, i.e total surface area, and lateral surface area. The total surface area of hemisphere = 3πr2
Lateral surface area of hemisphere = 2πr2
|The surface area of sphere = 4πr2|
Volume of a Hemisphere
The volume of a hemisphere is the total capacity of the hemisphere and it is the number of unit cubes covered inside that area. The unit of hemisphere volume is cubic units and is expressed as m3, cm3, in3, etc. Therefore, the formula to find the volume is:
Volume of Hemisphere = (2πr3)/3
Where π is the constant measuring 3.142 approx. or 22/7, and r is the radius of the hemisphere. For detailed information, you can check out this article Volume of Hemisphere.
Surface Area of a Hemisphere
The surface area of a hemisphere can be calculated by the area of its circular base with its curved surface. The hemisphere can either be hollow or a solid, according to that the surface area can be calculated. It is measured in square units and the formula is:
Surface Area of Hemisphere = 3πr2
Where π is the constant measuring 3.142 approx., and r is the radius of the hemisphere. For detailed information, you can check out this article Surface Area of a Hemisphere.
Lateral Area of a Hemisphere
The curved surface of a hemisphere is considered the lateral area of a hemisphere. If the radius is given, we can find out the lateral surface area using the formula and it is measured in square units. The formula for finding the lateral area is:
Lateral Area of a Hemisphere = 2πr2
Where π is the constant measuring 3.142 approx., and r is the radius of the hemisphere. For detailed information, you can check out this article Curved Surface Area of a Hemisphere
Related Topics on Hemisphere
Listed below are a few interesting topics that are related to the hemisphere:
Example 1: Which of these shows as a hemisphere - a, b, c, or d?
Solution: Figure c is a hemisphere as it has one curved side and one flat side. A hemisphere is a 3D figure that is half of a sphere. The other figures are triangle (a), semicircle (b), and cylinder (d).
Example 2: Emily is having porridge in a hemispherical bowl for fruits. The radius of the bowl is 4 inches. What is the volume of the fruit bowl? (put pi = 22/7)
Solution: The volume of a hemisphere is half the volume of the sphere. So, the volume of the hemisphere is given by (2πr3)/3. Let's calculate the volume of the bowl.
Volume of the hemisphere shaped bowl = (2πr3)/3
Volume = (2 × 22 × 43) / (7 × 3)
Volume = 2816/21
Volume = 134.09 inches3
Therefore, the volume of the fruit bowl is 134.09 inches3
FAQs on Hemisphere
What is a Hemisphere?
A hemisphere is a 3D figure which is obtained by cutting a sphere into two equal halves through its diameter. The hemisphere has one curved side and one flat side called the face of the hemisphere or the great circle of the sphere which helps in forming the hemisphere. Some of the real-life examples of a hemisphere are a bowl, igloo, the top part of a mushroom, etc.
What is the Formula to Find the Volume of a Hemisphere?
The volume of a hemisphere is expressed in cubic units and the formula is Volume of Hemisphere = (2πr3)/3, where π is the constant measuring 3.142 approx or 22/7, and r is the radius of the hemisphere.
What is the Formula to Find the Surface Area of a Hemisphere?
The surface area of a hemisphere is the curved part of the hemisphere and we calculate it by using this formula, Surface Area of Hemisphere = 3πr2, where π is the constant measuring 3.142 approx or 22/7, and r is the radius of the hemisphere. Note that this is the total surface area of the hemisphere which including the area of the base too.
What is the Formula to Find the Lateral Area of a Hemisphere?
If the radius of a hemisphere is mentioned, we can calculate the lateral area of a hemisphere by using this formula, Lateral Area of a Hemisphere = 2πr2, where π measures 3.142 approx or 22/7, and r is the radius of the hemisphere. The lateral area is the area of the curved part of the hemisphere only. It does not include the area of the base which is in the shape of a circle.
Are Sphere and Hemisphere the Same?
The sphere and hemisphere are very similar in properties since the hemisphere is made from a sphere. When a sphere is cut into two equal halves, these two halves are called a hemisphere. But one of the main differences between a sphere and a hemisphere is that a sphere does not have any flattened end but only curves whereas a hemisphere has one flattened end and one curved surface.
What is a Hollow Hemisphere?
The empty space inside the hemisphere is called a hollow hemisphere. The radius in a hollow hemisphere is different from the internal and external. The hollow hemisphere is considered to have to be thicker at the circumference compared to the normal hemisphere.
What is the Formula for the Base Area of a Hemisphere?
In a hemisphere, if its radius (r) is given, then its base area is given as Base Area of a Hemisphere = Area of the base circle = πr2