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The term hemisphere came from the books of mathematics. Yes, the hemisphere is related to the subject of mathematics. Hemisphere is a shape commonly used in our daily life, and the surroundings as a bowl used in the kitchen is a hemisphere. The mushroom shape is like a hemisphere, hat, cake, igloo, ice cream, and many more examples. Hemisphere is considered a three-dimensional shape. Hemisphere is exactly half of the sphere, in which one side is flat, and the other is circular. So now we shall talk about the properties of a hemisphere and the curved surface area. Let’s start with the curved surface area of the hemisphere.
Area of hemisphere
When we pick a sphere and cut it into two halves, we can obtain a hemisphere. The one surface of the hemisphere is always flat, and the other surface is circular. There are various examples of hemispheres in our real life and surrounding, as the planet on which we live is also a sphere, and if we cut the earth into equal two halves, we shall obtain the Area of the hemisphere from there. Even the earth’s hemispheres are also important from a geographical point of view. Now the hemisphere doesn’t always need to be vacant or solid. There is a probability of both shapes. If the flat side of the hemisphere is not solid, it may be hollow or vacant; then, it is not a solid hemisphere. Here hollow means space or vacant. If there is no hollow or space on the flat side of the Hemisphere, then it is a solid hemisphere.
There are two types of the Area of the hemisphere that we determine in mathematics. The surface area is meant by the area occupied by the solid. So one is curved surface area, and the other is total surface area. Curved surface area is determined when the hemisphere is the hollow type, and the total surface area is determined when the hemisphere is not the hollow type/solid type.
The curved surface area of the hemisphere:
As we already discussed, the hemisphere is considered to be exactly 0.5 of the shape of the sphere, so the C.S.A of the hemisphere is also half of the C.S.A of the sphere. The C.S.A. of the sphere is 4πr^2.
So the curved surface area of the hemisphere is half of 4πr^2. That is ½(4πr^2) = 2πr^2.
So the formula to determine the C.S.A. is 2πr^2. When we determine the C.S.A of the hemisphere, then we don’t consider the area of flat surface area in the C.S.A. In simpler words, the curved surface area of the hemisphere is the total surface area of the hemisphere except for the area of the flat side or base of the hemisphere.
Total Surface Area of the Hemisphere:
Besides the curved surface area of the hemisphere, now we shall determine the total surface area of the hemisphere. The total Surface area of the hemisphere is the total curved surface area of the hemisphere and the area of the flat surface or base of the hemisphere, which is circular. So the area of the circle is always πr^2. The curved surface area of the hemisphere is 2πr^2. So now we shall add both the areas and will determine the total surface area of the hemisphere is
(2πr^2 + πr^2 = 3πr^2)
3πr^2 is the total surface area of the hemisphere.
If we focus on determining the surface area of the hollow hemisphere, then there are two points to consider. As there will be some thickness in the hollow hemisphere, that thickness will alter the hemisphere’s surface area. What you have to do is measure the two radii of the hemisphere. One radius should be from the centre of the hemisphere to the end of the hemisphere or external hemisphere. Another radius should be from the centre of the Hemisphere to the internal hemisphere.
The area of the Hollow Hemisphere is equal to the area of the external Hemisphere and the area of the Internal Hemisphere.
Conclusion:
So in this article, we have discussed the curved surface area of the hemisphere. Besides that, we have discussed the total surface area of the hemisphere also. Hemisphere is the shape we read in mathematics and frequently use in our daily real life. Around us, everything has a shape; some things are spherical, some are conical, rectangular, circular, squoval, oval, etc. The study of the hemisphere is also very important and enriching from the mathematics point of view. These are the basic details about the hemisphere that we all should know because the hemisphere is a very common shape that is used.
