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143 LearnersLast updated on September 4, 2025
Surface Area of Hemisphere
A hemisphere is a three-dimensional shape that represents half of a sphere. The surface area of a hemisphere includes both the curved surface and the circular base. In this article, we will learn about the surface area of a hemisphere.
What is the Surface Area of a Hemisphere?
The surface area of a hemisphere is the total area occupied by the boundary or surface of a hemisphere. It is measured in square units.
A hemisphere has a curved surface and a flat circular base, so it has two surface areas: the curved surface area and the total surface area. A hemisphere is essentially half of a sphere, split along its diameter.
Surface Area of a Hemisphere Formula
A hemisphere has a curved surface, which contributes to two types of surface areas: the curved surface area and the total surface area. Look at the hemisphere below to understand its surface area and radius (r).
A hemisphere has two types of surface areas:
- Curved Surface Area of a Hemisphere
- Total Surface Area of a Hemisphere
Curved Surface Area of a Hemisphere
The area of the curved part of the hemisphere, excluding its base, is known as the curved surface area of a hemisphere.
The formula for the CSA (Curved Surface Area) of the hemisphere is given as:
Curved Surface Area = 2πr² square units
Here, r is the radius of the base of a hemisphere.
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Total Surface Area of a Hemisphere
The total area occupied by the hemisphere, including the area of the curved surface and the area of the circular base, is known as the total surface area of the hemisphere.
The formula is: Total Surface Area = 3πr² square units
Where r is the radius of the base of the hemisphere.
Derivation of the Total Surface Area of a Hemisphere:
To find the total surface area of a hemisphere, consider both its curved surface and the base.
The base area of a hemisphere = πr².
Curved surface area of a hemisphere = 2πr².
By adding these, Total surface area = base area + curved surface area = πr² + 2πr² = 3πr²
Volume of a Hemisphere
The volume of a hemisphere shows how much space it contains. It is half of the volume of a sphere with the same radius.
The volume can be calculated using the formula: Volume = (2/3)πr³ cubic units
Confusion between CSA and TSA
Students sometimes confuse the curved surface area (CSA) and total surface area (TSA) of a hemisphere. Remember, CSA includes only the curved surface, while TSA includes both the curved surface and the base.
Mistake 1
Using diameter instead of radius
Some students mistakenly use the diameter instead of the radius. Ensure you use the radius (half of the diameter) when applying the formulas for surface area.
Mistake 3
Forgetting to include the base area in the total surface area
Students often calculate only the curved surface and forget to add the circular base. Always include both parts when calculating the total surface area. Total surface area = curved surface area + base area.
Mistake 4
Assuming curved surface area and lateral surface area are different
Some students mistakenly believe that curved surface area and lateral surface area are different, but in a hemisphere, they mean the same thing. Use the same formula for both.
Mistake 5
Solved Examples of Surface Area of Hemisphere
Find the curved surface area of a hemisphere with a radius of 7 cm.
CSA = 308 cmยฒ
Problem 1
Given r = 7 cm. Use the formula: CSA = 2ฯrยฒ = 2 ร (22/7) ร 7 ร 7 = 2 ร 22 ร 7 = 308 cmยฒ
Find the total surface area of a hemisphere with a radius of 5 cm.
Explanation
TSA = 235.5 cm²
Problem 2
Use the formula: TSA = 3ฯrยฒ = 3 ร 3.14 ร 5ยฒ = 3 ร 3.14 ร 25 = 3 ร 78.5 = 235.5 cmยฒ
A hemisphere has a radius of 6 cm. Find the total surface area.
Explanation
TSA = 339.12 cm²
Problem 3
Use the TSA formula: TSA = 3ฯrยฒ = 3 ร 3.14 ร 6ยฒ = 3 ร 3.14 ร 36 = 3 ร 113.04 = 339.12 cmยฒ
Find the curved surface area of a hemisphere with a radius of 3.5 cm.
Explanation
CSA = 77 cm²
Problem 4
CSA = 2ฯrยฒ = 2 ร (22/7) ร 3.5 ร 3.5 = 2 ร 22 ร 0.5 ร 3.5 = 2 ร 11 ร 3.5 = 77 cmยฒ
The curved surface area of a hemisphere is 660 cm². Find the radius.
Explanation
Radius = 10 cm
It is the total area that covers the outside of the hemisphere, including its curved surface and the base.
1.What are the two types of surface area in a hemisphere?
2.How does the curved surface area differ from the total surface area?
3.Is curved surface area the same as lateral surface area?
4.What unit is surface area measured in?
Common Mistakes and How to Avoid Them in the Surface Area of a Hemisphere
Students often make mistakes while calculating the surface area of a hemisphere, leading to incorrect answers. Below are some common mistakes and ways to avoid them.
Seyed Ali Fathima S
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Seyed Ali Fathima S a math expert with nearly 5 years of experience as a math teacher. From an engineer to a math teacher, shows her passion for math and teaching. She is a calculator queen, who loves tables and she turns tables to puzzles and songs.
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