Area Of Hemisphere

The total surface area of a hemisphere is another name for a hemisphere's surface area. The sum of all the faces makes up a hemisphere's total surface area (curved and base area). When a sphere is split into two equally sized parts by a plane, a hemisphere is created. In geometry, a hemisphere is the exact opposite of a sphere, to put it another way. Hemi, which means half, and sphere, a 3D mathematical shape, make up this object. Two equal hemispheres are produced when a sphere is split down the middle along its diameter.

Hemisphere

A sphere is a three-dimensional solid in which the distances between all points on its surface and its center are equal. When the sphere is divided into two equal halves by the plane, a hemisphere is created. The two hemispheres come together to form a sphere.

Curved Surface Area Of Hemisphere

A hemisphere's curved surface area is the area that is covered by its curved surface. It has a surface area that is exactly half that of a sphere. The formula below can be used to determine the curved surface area of a hemisphere with radius r.

Curved surface area of a hemisphere = 12(curved surface area of a sphere) = 1/2(4πr2)=2πr2

Where, r is the radius of the hemisphere.

Total Surface Area Of Hemisphere

The combined space filled by the curved surface and the base surface of the hemisphere is referred to as the hemisphere's total surface area. By adding the areas of a hemisphere's base surface and curved surface, the total surface area of a hemisphere can be determined. It should be noticed that a hemisphere has a circle for its base. If a hemisphere's radius is known, the following formula can be used to determine its total surface area:

Total surface area of a hemisphere = Curved Surface Area + Base Area = 2πr2 + πr2 = 3πr2

Hollow Hemisphere

A hollow sphere can be defined as the sphere that has been thinned out to the point that a wall of equal thickness produces an interior ball with radius ‘r’ inside the exterior ball with the radius ‘R’.

Surface Area Of The Hollow Hemisphere

The formula for a hollow hemisphere's surface area is TSA of hollow hemisphere = 3R2 + r2.

It should be noted that a hollow hemisphere has two diameters for its circular bases: one for the inner base (the hollow region) and one for the outer base. The following formulas can be derived if "r" is the radius of the internal hemisphere and "R" is the radius of the external hemisphere.

• The outer hemisphere's curved surface area is equal to 2R2.

• The inner hemisphere's curved surface area is equal to 2r2.

• If we observe the figure given above, we can see that a ring is formed. The Area of the formed ring = π(R2 - r2)

• The Total surface area of the hollow hemisphere can be calculated if we add the formulas given above, that is, TSA of a hollow hemisphere = 2πR2 + 2πr2 + π(R2 - r2). This can be written as, TSA of hollow hemisphere = 2π(R2 + r2) + π(R2 - r2). And if we want to simplify it further, it becomes 3πR2 + πr2