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We can define a hemisphere as half of a sphere. Aspherical, in general, produces exactly two hemispheres. Our planet is an excellent example of a hemisphere. A Hemisphere is formed by cutting a sphere in half. As a result, the volume of a hemisphere of the same size is half that of a sphere of the same size. As a result, the volume of a hemisphere Equals 2/3π r3. The entire space enclosed by any 3-dimensional item or solid form is defined as the volume of a 3-d shape. Alternatively, it may be described as the number of unit cubes that can be crammed into a given geometry. Cubic metres are the SI unit of volume.
Volume of Hemisphere
A hemisphere’s volume is the amount of space occupied by the Hemisphere. A greater volume object takes up more room. A hemisphere is a 3D object half the size of a whole spherical object, such as bowls, headphones, Igloos, domes in architecture, etc. As a result, the volume of a hemisphere is half that of a sphere. Let us learn how to calculate the volume of a hemisphere using a few answered examples and practice problems.
How to Find Volume of a Hemisphere?
A hemisphere is a three-dimensional form half the size of a sphere. A hemisphere is the shape formed when a sphere is sliced by a plane travelling through its centre. A hemisphere has one flat circular base and one curved surface.
The volume of a Hemisphere is the Hemisphere’s capacity or the amount of space it occupies. The volume is measured in cubic units. A hemisphere’s volume may be computed as follows:
The volume of the hemisphere formula is 2/3π r^3, where ‘r’ is the radius of the Hemisphere.
Some Solved Examples to find the volume of Hemisphere:
- Find the volume of a hemisphere-shaped bowl with a radius measuring seven units?
Solution:The volume of a bowl = 2/3 ×π × r^3
= 2/3 ×3.14 × 73
= 2/3 × 3.14 × 7× 7 × 7
= 718.013 cubic units
Therefore, the volume of a bowl = 718.013 cubic units
- Find the volume of the cap, which is in hemisphere shape with a radius measuring 11 cm. (Take π = 3.14)
Solution:
It is given that the radius of the cap is = 11 cm
To find the volume of the cap, we need to apply the volume of the hemisphere formula, i.e. 2/3π r^3.
Putting the value ‘r’ as 11, we get
Volume of a cap = (2π × 113)/3
Volume of a cap = (2 × 3.14 × 113)/3
Hence, the volume of the Hemisphere is 2786.27 units3.
- The radius of a hemisphere is 4.5 inches. What is the volume of the Hemisphere? (Take pi = 3.14)
Solution:
The volume of a hemisphere is half the volume of the sphere.
So using the volume of a hemisphere formula,
The volume of the Hemisphere = 2/3π r^3.
After putting the value of r = 4.5, we get,
Volume of the hemisphere = 2πr^3/3 = = (2 × 3.14 × (4.5)3)/3 = 191.36 cubic inches.
Therefore, the volume of the Hemisphere is 191.36 cubic inches.
- A sphere of radius 14 cm is cut into two halves. Find the volume of each Hemisphere that is formed.
Solution:
The radius of the Hemisphere so formed is,
Radius of hemisphere, r = 14 cm
We know that Volume of hemisphere = 2πr^3/3 = (2 × 3.14 × 143)/3 = 5744.106 cm3.
Therefore, the volume of each Hemisphere = 5744.106 cm3
Introduction to Hollow Hemisphere: A hollow hemisphere has two circular base diameters, one for the interior circular base (hollow section) and the exterior circular base (rigid part). As a result, the area of the hollow Hemisphere equals the difference between the areas of the exterior and interior hemispheres.
How to find the volume of the Hollow Hemisphere?
The volume of a hollow hemisphere is denoted by: Volume = 2/3 𝜋R^3 – 2/3 𝜋r^3, where R is the radius of the outer sphere and r is the radius of the inside Hemisphere.
Find out the volume of the hollow Hemisphere with an outer radius equal to 6 cm and an inner radius equal to 4cm.
Explanation :
Given outer radius = R = 6cm
Inner radius = r = 4cm
Volume = 4/3 π(R^3-r^3)
= 2/3*3.14*(216-64)
=2/3*3.14* 152
= 318.186 cm3 ans.
Conclusion:
After reading this article, you will have a clear knowledge of the notion of the volume of the Hemisphere and the volume of the hollow Hemisphere. You will be more aware of repeating forms in your surroundings. Your research to present your results to the class will improve your grasp of volume principles and how they correlate to the sizes of specific real-world items. Once you learn the formula, you can easily find the volume. Sometimes solving hollow hemispheres can be a little tricky, but practice will make it easy too. Be careful when you are asked to find the volume of any object. It may get confusing sometimes.
