Volume of Hemisphere
The volume of a hemisphere is the space occupied by the hemisphere. An object with a larger volume occupies more space. A hemisphere is a 3D object which is half of a full sphere, for example bowls, headphones, Igloo, domes in architecture, etc. Therefore, the volume of a hemisphere is half the volume of a sphere. Let us learn how to find the volume of the hemisphere with the help of a few solved examples and practice questions.
| 1. | What is the Volume of a Hemisphere? |
| 2. | Volume of a Hemisphere Formula |
| 3. | How to Find the Volume of Hemisphere? |
| 4. | FAQs on Volume of Hemisphere |
What is the Volume of a Hemisphere?
A hemisphere is a three-dimensional shape (3D shape) that is half of a sphere. When a sphere is cut by a plane passing through its center, the shape that we get is called the hemisphere. A hemisphere has a curved surface and one flat circular base. The volume of a hemisphere is the number of unit cubes that can fit into it. The unit of volume is cubic units, therefore, the volume of a hemisphere can be expressed as m3, cm3, in3, and so on.
Let us learn more about the formula of the volume of a hemisphere.
Volume of a Hemisphere Formula
The volume of a hemisphere is half the volume of a sphere, therefore, it is expressed as,
Volume of hemisphere = 2πr3/3, where r is the radius of the hemisphere.
Let us see how the formula for the volume of a hemisphere is derived. Since a hemisphere is half of a sphere, we can divide the volume of a sphere by 2 to get the volume of its hemisphere. Now considering that the radius of a sphere is r.
Volume of the sphere can be calculated using the formula, Volume of Sphere = 4πr3/3. So, the volume of a hemisphere = 1/2 of 4πr3/3 = 1/2 × 4πr3/3 = 2πr3/3
How to Find the Volume of a Hemisphere?
The volume of a hemisphere is calculated using the formula, Volume of hemisphere = 2πr3/3. So, let us find the volume of a hemisphere which has a radius of 7 units.
- Step 1: Note the radius of a hemisphere. Here, radius (r) = 7 units.
- Step 2: Substitute the value of the radius in the formula, Volume of hemisphere = 2πr3/3 and represent the final answer with cubic units.
- Step 3: After substituting the value of r = 7, we get, Volume of hemisphere = 2πr3/3 = (2 × 3.14 × 73)/3 = 718.01 cubic units.
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FAQs on the Volume of Hemisphere
What is the Volume of Hemisphere?
The volume of a hemisphere is defined as the total space covered by the 3-D shape in a three-dimensional plane. The volume of a hemisphere is expressed in cubic units, cm3, m3, ft3, etc.
What is a Hemisphere?
A hemisphere is a three-dimensional shape that is half of a sphere. When we cut a sphere into two halves, then the shape that we get is called the hemisphere.
How to Find the Volume of a Hemisphere?
The volume of a hemisphere can be calculated by using the formula, Volume of a hemisphere = 2πr3/3; where 'r' is the radius of the sphere.
What is the Formula for the Volume of a Hemisphere?
The formula which is used to calculate the volume of a hemisphere is expressed as, Volume of hemisphere = 2πr3/3, where r is the radius of the hemisphere.
What Units are Used with the Volume of a Hemisphere?
The volume of a hemisphere is expressed in square units. In the metric system of measurement, the most common units of volume of a hemisphere are cubic meters, cubic inches, milliliters, and liters.
How to Find the Volume of a Sphere?
The formula that is used for the volume of a sphere is, Volume of Sphere = 4πr3/3, where r is the radius of the sphere.
What is the Volume of a Hemisphere that has a Diameter of 12.6 units?
If the diameter of a hemisphere is 12.6 units, its radius will be 12.6 ÷ 2 = 6.3 because diameter = 2 × radius. Now, we can apply the formula which is, volume of a hemisphere = 2πr3/3. After substituting the value of r = 6.3 we get, volume of a hemisphere = 2πr3/3 = (2 × 3.14 × 6.33)/3 = 523.4 cubic units.