Surface Area of a Hemisphere
The surface area of a hemisphere is defined as the region covered by the total surface of the solid object. The surface area of a hemisphere can be classified as the total surface area and the curved surface area. In this section, we will discuss the surface area of a hemisphere, both total surface area and the curved surface area along with solved examples.
1.  What is the Surface Area of Hemisphere? 
2.  Surface Area of a Hemisphere Formula 
3.  How To Find the Surface Area of a Hemisphere? 
4.  FAQs on the Surface Area of a Hemisphere 
What is the Surface Area of Hemisphere?
The surface area of a hemisphere is given as the area covered by the surface of a hemisphere. Hemisphere is a threedimensional shape, obtained when a sphere is cut along a plane passing through the center of the sphere. In other words, a hemisphere is half of a sphere. The hemisphere can either be hollow or solid. The surface area of a hemisphere is measured in square units.
Surface Area of a Hemisphere Formula
The formula for the surface area of a hemisphere can be given for a solid as well as for a hollow hemisphere. The surface area of a hemisphere is the total area its surface covers. It can be classified into two categories:
 The curved surface area of a hemisphere(CSA)
 The total surface area of a hemisphere(TSA)
Curved Surface Area of a Hemisphere(CSA) Formula
The curved surface area of a hemisphere is the area covered by the curved surface of the solid. It is exactly half of the surface area of a sphere. The curved surface area of a hemisphere with radius 'r' can be calculated using the following formula.
Curved surface area of a hemisphere = 1/2 (curved surface area of a sphere) = 1/2 (4 π r^{2}) = 2 π r^{2}
Where, r is the radius of the hemisphere.
Total Surface Area of a Hemisphere(TSA) Formula
The total surface area of the hemisphere is defined as the total space occupied or covered by the curved surface and the base surface of the hemisphere. The total surface area of a hemisphere can be calculated by finding the sum of the areas of its curved surface and base surface. For a hemisphere, if its radius is given, then its surface area can be given by:
Surface area of a hemisphere = Curved Surface Area + Base Area = 2 π r^{2} + π r^{2} = 3 π r^{2}
Where, r is the radius of the hemisphere.
Surface Area of a Hollow Hemisphere Formula
There are two diameters for the circular bases of a hollow hemisphere, one for the inside circular base(hollow region), and one for the outside circular base. Therefore, the area of the hollow hemisphere can be given as,
Curved surface area of outer hemisphere = 2π \(r_2\)^{2}
Curved surface area of inner hemisphere = 2π \(r_1\)^{2}
Area of ring = π(\(r_2\)^{2} – \(r_1\)^{2})
Total surface area of hollow hemisphere, TSA = 2π \(r_2\)^{2 }+ 2π\(r_1\)^{2 }+ π(\(r_2\)^{2} – \(r_1\)^{2})
TSA = 2π (\(r_2\)^{2 }+ \(r_1\)^{2}) + π(\(r_2\)^{2} – \(r_1\)^{2})
TSA = 3π\(r_2\)^{2} + π\(r_1\)^{2}
Where,
 \(r_1\) is the radius of the internal hemisphere, and
 \(r_2\) is the radius of the external hemisphere.
How To Find the Surface Area of a Hemisphere?
As we learned in the previous section, the surface area of a hemisphere can be calculated using different formulas for hollow or solid hemisphere, depending on whether we are finding the curved surface area or the total surface area.
Curved Surface Area of Hemisphere
The formula to calculate the curved surface area of a hemisphere with radius 'r' is given as 2πr^{2}. Thus, we follow the steps shown below to find the total area of a hemisphere.
 Step 1: Identify the radius of the hemisphere and name it to be r.
 Step 2: Find the surface area of a hemisphere using the formula = 2πr^{2}.
 Step 3: Represent the final answer obtained with square units.
Total Surface Area of Hemisphere
The formula to calculate the total surface area of a hemisphere with radius 'r' is given as 3πr^{2}. Thus, we follow the steps shown below to find the total area of a hemisphere.
 Step 1: Identify the radius of the hemisphere and name it to be r.
 Step 2: Find the total surface area of a hemisphere using the formula = 3πr^{2}.
 Step 3: Represent the final answer obtained with square units.
Surface Area of Hollow Hemisphere
The following steps can be calculated to find the surface area of a hollow hemisphere,
 Step 1: Identify the inner and outer radius of the hollow hemisphere, and name them as \(r_1\) and \(r_2\) respectively.
 Step 2: Find the total surface area of the hemisphere using the formula, (3π\(r_2\)^{2 }+ π\(r_1\)^{2})
 Step 3: Represent the final answer obtained with square units.
Example: Find the surface area of a hemisphere whose radius measures 7 units. (Use π = 22/7)
Solution:
The radius of the hemisphere = 7 units
Surface area of a hemisphere = 3 π r^{2} = 3 (22/7) 7^{2} = 3 × 22 × 7 = 462 units^{2}
Therefore, the surface area of the hemisphere = 462 units^{2}
Let us have a look at a few solved examples to understand the area of a hemisphere better.
Examples of Surface Area of a Hemisphere

Example 1: Find the total surface area of a hemisphere with radius = 21 units. (Use π = 22/7)
Solution:
Radius of the hemisphere = 21 units
Using total surface area of a hemisphere formula,
Total surface area of a hemisphere = 3 π r^{2} = 3 (22/7) 21^{2} = 3 × 22 × 21 × 3 = 4158 units^{2}Therefore, the total surface area of the hemisphere = 4158 units^{2}

Example 2: Using the surface area of a hemisphere formula, find the radius of the hemisphere given its total surface area = 462 units^{2}. (Use π = 22/7)
Solution:
The total surface area of a hemisphere = 462 units^{2}
3 π r^{2} = 462
r^{2} = 462/(3π) = 49
r = 7 units
Therefore, the radius of the hemisphere = 7 units
FAQs on the Surface Area of a Hemisphere
How Do You Find the Surface Area of a Hemisphere?
The surface area of a hemisphere can be calculated using different formulas for the hollow and solid hemisphere, depending upon the area being curved or total surface area.
 The total surface area of a hemisphere = 3πr^{2}
 The curved surface area of a hemisphere = 2πr^{2}
 The total surface area of a hollow hemisphere = 2π (\(r_2\)^{2 }+ \(r_1\)^{2}) + π(\(r_2\)^{2} – \(r_1\)^{2}) (or) 3 π \(r_2\)^{2} + π \(r_1\)^{2}
Where, 'r' is the radius of the sphere, \(r_1\) is the radius of the internal hemisphere, and \(r_2\) is the radius of external hemisphere
What is the Total Surface Area of a Hollow Hemisphere?
The total space occupied or covered by the curved surface and the base surface of the hemisphere is defined as the total surface area of a hemisphere. For a hollow hemisphere, if its inner radius (r) and outer radius (R) are given, then its area can be given by: total surface area of a hollow hemisphere = outer curved surface area + inner curved surface area + base area
TSA = 2 π R^{2} + 2 π r^{2} + π (R^{2}  r^{2})
TSA = 3 π R^{2} + π r^{2}
What is the Base Area of a Hemisphere?
For a hemisphere, if its radius (r) is given, then its base area can be given by: base area of a hemisphere = area of the base circle = π r^{2}
What is the Lateral Surface Area of a Hemisphere?
The lateral surface area of a hemisphere is the region bounded by the curved surface of the hemisphere. For a hemisphere, if its radius (r) is given, then its lateral surface area can be given by: lateral surface area = 1/2 (lateral surface area of a sphere) = 1/2 (4 π r^{2}) = 2 π r^{2}
What is the Total Surface Area of Hemispherical Shell?
Total surface area of a hemispherical shell can be found using the formula, TSA = 2π (\(r_2\)^{2 ;}+ \(r_1\)^{2}) + π(\(r_2\)^{2} – \(r_1\)^{2}) (or) 3 π \(r_2\)^{2} + π \(r_1\)^{2}, where, \(r_1\) is the radius of internal hemispherical shell, and \(r_2\) is the radius of external hemispherical shell.
What is the Formula of Total Surface Area of a Hollow Hemisphere?
Total surface area of a hollow hemisphere shell can be calculated using the formula, TSA = 2π (\(r_2\)^{2 }+ \(r_1\)^{2}) + π(\(r_2\)^{2} ndash; \(r_1\)^{2}) (or) 3 π \(r_2\)^{2} + π \(r_1\)^{2}, where, \(r_1\) is the radius of internal hemisphere, and \(r_2\) is the radius of external hemisphere.
What is the Difference Between Curved Surface Area and Surface Area of Hemisphere?
The curved surface area (CSA) is that part of the hemisphere that is curved. Whereas, the surface area of the hemisphere covers the curved area and the rest of the area of the hemisphere. Hence, the formula to calculate the curved surface area is 2πr^{2} and the surface area or the total surface area of the hemisphere is 3πr^{2}.
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