A hemisphere is obtained when we cut the sphere into two equal halves. The total surface area of hemisphere will be equal to the sum of its curved surface area and the base area of hemisphere. The base is in circular shape here. We can find various real-life examples of the hemispheres such as our planet Earth can be divided into two segments the southern & northern hemispheres.
|Surface Area of Hemisphere = 3 π r2|
The Hemispheres can either be of a solid type or can be hollow.
Surface Area of Hemisphere
The surface area is the area occupied by the surface of the solid object. The surface area is classified into two types, namely;
- Curved Surface Area (CSA)
- Total Surface Area (TSA)
Curved Surface Area
As the Hemisphere is the half part of a sphere, therefore, the curved surface area is also half that of the sphere.
Curved surface area of hemisphere = 1/2 ( 4 π r2) = 2 π r2
The base of the hemisphere is in circular shape. As we know by the formula of area of circle,
Area of base = π r2
Total Surface Area
The total surface area of the hemisphere– While calculating the total surface area of a hemisphere, we need to consider the base of the hemisphere which is circular. Thus, the total surface area of a hemisphere is equal to:
Total Surface Area (TSA) = Curved Surface Area + Area of the Base Circle
= 2 π r2 + π r2
= 3 π r2
Area of Hollow Hemisphere
A hollow hemisphere has two diameters for its circular bases, one is for inside circular base (hollow part) and one is for outside circular base (rigid part). Therefore, the area of hollow hemisphere is equal to the difference between area of external hemisphere and area of internal hemisphere.
Area of Hollow Hemisphere = Area of External Hemisphere – Area of Internal Hemisphere
From the above figure, we can see, r1 is the radius of internal hemisphere and r2 is the radius of external hemisphere.
We can derive the formula by adding the curved surfaces of outer hemisphere, inner sphere and the ring formed between them.
Curved Surface of outer hemisphere = 2π r22
Curved Surface of inner hemisphere = 2π r12
Area of the ring = π(r22 – r12)
Therefore, total area of hollow hemisphere is:
TSA = 2π r22 + 2π r12 + π(r22 – r12)
TSA = 2π (r22 + r12) + π(r22 – r12)
Real-Life Examples of Hemisphere
In the pictures given below, bowl and coconut shells are examples of hollow-hemisphere.
This is all about the area formulae of the Hemispheres. To know more about the other geometrical shapes and to find Surface Areas and Volume, visit our site BYJU’S.