Area Of Hemisphere

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.

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

Base Area

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.

Coconut Shell

Bowl

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.

Video Lesson

Solved Examples on Area of Hemisphere

Example 1:

Find the total surface area of the hemisphere whose base radius is 3 cm (take 𝜋 = 3.14). 

Solution:

Base radius of the hemisphere = 3 cm

The total surface area of a hemisphere = 3𝜋r²

= 3 × 3.14 × 3²

= 84.78 cm².

Example 2:

Find the total surface area of a hollow hemisphere whose inner and outer radii are 7 cm and 8 cm, respectively.

Solution:

Let the inner and outer radii of the hemisphere be r1 and r2, respectively. 

Then r₁ = 7 cm and r₂ = 8 cm

The total surface area of a hollow cylinder = 2𝜋(r₂² + r₁²) + 𝜋(r₂² – r₁²) 

= 2𝜋 (8² + 7²) + 𝜋(8² – 7²)  

= 2𝜋 (64 + 49) + 𝜋(64 – 49)

= 2𝜋 × 113 + 15𝜋

= 241𝜋 cm².

Example 3:

Find the base area of a cylinder whose curved surface area is 256 cm².  

Solution:

Let r be the radius of the hemisphere.

The curved surface area of a hemisphere = 2𝜋r² = 256 cm²

Base radius of the hemisphere = 𝜋r² = CSA of hemisphere/2 = 256/2 = 128 cm².

Practice Questions on Area of Hemisphere

1. Find the total surface area of a solid hemisphere whose volume is 19,404 cm³. 
2. Find the surface area of a hollow hemisphere whose inner and outer diameter is 12 cm and 14 cm, respectively.
3. Find the capacity of a hemispherical bowl whose curved surface area is 344 cm².