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Hemisphere is a three-dimensional shape generated by dividing a sphere into two halves. It is a half-spherical curve combined with a planar circular area. Generally, a hemisphere refers to half of the Earth, such as the northern or southern hemispheres. In geometry, however, a hemisphere is a 3D shape formed by splitting a sphere into two halves, each with one flat side. In everyday life, we come across various items that have the form of a hemisphere. For example, if we cut a cherry in half, we obtain a hemisphere-shaped cherry. In this article, we’ll study more about hemispheres, their properties, formulas, and others in detail.
Table of Content What is Hemisphere?Hemisphere is a 3D shape which consist of a curved and a plane surface and resembles the shape of a bowl. Hemisphere means Half of Sphere. The word hemisphere is made up of two parts: hemi, which means half, and sphere, which is a mathematical 3D form in mathematics. A hemisphere is made by carefully cutting a sphere along its diameter, leaving two identical hemispheres behind. The flat side of the hemisphere is the base or face of the hemisphere. Hemispheres can be either hollow or solid. Definition of Hemisphere
Elements of a HemisphereVarious Elements of Hemisphere are,
Properties of HemisphereSome important properties of Hemisphere are,
Volume of HemisphereThe Volume of Hemisphere is determined by using the formula of volume of a sphere. The formula is used to compute the volume of a sphere, where r is the radius of the sphere.
To get the volume of a hemisphere, divide the volume of a sphere in half. The volume of a hemisphere formula is shown below for a hemisphere with radius, r.
where, r is the radius of the hemisphere and the value of π is 22/7 or 3.142. Hemisphere Surface AreaA hemisphere’s surface area is derived from that of a sphere and may be determined using particular methods. For a hemisphere with radius r, the total surface area comprises both the curved and base areas. Since, hemisphere has both plane and curved surfaces hence it has two types of surface areas mentioned below:
Curved Surface Area of a HemisphereCurved surface area of a hemisphere is based on the surface area of a sphere. We know that surface area pf sphere is given as:
We know that hemisphere is half of sphere therefore, we divide the sphere’s surface area in half to get the curved surface area of the hemisphere.
where, r is the radius of the hemisphere and the value of π is 22/7 or 3.142 Total Surface Area of a HemisphereTotal Surface Area of hemisphere consist of curved as well as planar surface area of hemisphere. If we want the total surface area, we must add the base area to the curved surface. The area of the circle base is provided by πr2 and curved surface area is 2πr2 Here is the formula for calculating the surface area of a hemisphere of radius r.
where, r is the radius of the hemisphere and the value of π is 22/7 or 3.142. Hollow HemisphereA hollow hemisphere has two surfaces: an interior and exterior surface. As a result, a hollow hemisphere will have two separate radii, namely inner radii and outer radii. The thickness of a hollow hemisphere is defined as the difference between the radii of the inner and outer radii of a hollow hemisphere. A hollow hemisphere’s area may be divided into two categories:
Curved Surface Area of Hollow HemisphereA hollow cylinder has two surfaces: an inner surface and an outer surface. It also has two radii, r for the inner hemisphere and R for the outer hemisphere. Inner hemisphere curved surface area: 2πr12 Outer hemisphere curved surface area: 2πr22
Total Surface Area of Hollow HemisphereA hollow hemisphere’s total surface area is the sum of the base of the circular ring and the curved surface areas of the inner and outer surfaces.
Volume of Hollow HemisphereThe volume of a hollow hemisphere is calculated by subtracting the volume of the smaller hemisphere (carved out) from the volume of the bigger hemisphere. To calculate the volume of a hollow hemisphere with outer radius R and inner radius r, use the following formula:
Hemisphere FormulasHere are some essential formulae for the surface area and volume of hemispheres, presented in a tabular format:
Hemisphere Shape ExamplesHemispheres can be seen in following examples in everyday life.
These forms are all around us, from dishes to fruit slices. They seem like half-balls or domes that we see all the time, whether in the kitchen or out and about. Difference Between Hemisphere and SphereVarious important differences between Hemisphere and Sphere are,
Also Read,
Hemisphere Formula Solved ExamplesExample 1: Determine the total surface area for a hemisphere having a radius of 25 cm. Solution:
Example 2: Determine the volume of a hemisphere having a radius of 22.6 inch. Solution:
Example 3: The radius of a hemisphere is 15.4 cm. Determine its curved surface area. Solution:
Example 4: What is the volume of water that a hemispherical bowl with a radius of 18 cm can hold? Solution:
Example 5: If the area of the hemispherical bowl’s base is 201.14 unit square, find its radius. Solution:
Practice Questions on HemisphereQ1. The radius of a hemisphere is 12 meters. Determine its total surface area. Q2. Determine the volume of a 5.8-centimeter-radius hemisphere. Q3. Determine the curved surface area of a 9.5-inch-radius hemisphere. Q4. The radius of a hemispherical tank is 30 feet. How much liquid can it hold? Q5. Determine the total surface area of a 7.2-meter-radius hemisphere. Q6. A fountain features a 14-inch-radius hemispherical bowl. Determine the amount of water it can hold. Hemisphere Frequently Asked QuestionsDefine Hemisphere.
What are the 4 hemispheres of the Earth?
What shape is a Hemisphere?
What are Sphere and Hemisphere?
What is Hemisphere Formula?
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| Class 9 |
Type: | Geek |
Category: | Coding |
Sub Category: | Tutorial |
Uploaded by: | Admin |
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