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126 LearnersLast updated on August 30, 2025
Surface Area of Hemispherical Dome
A hemispherical dome is a 3-dimensional shape that has a circular base and a curved half-sphere top. The surface area of the hemispherical dome is the total area covered by its outer surface. The surface area of the dome includes both its curved surface and its base. In this article, we will learn about the surface area of a hemispherical dome.
What is the Surface Area of a Hemispherical Dome?
The surface area of a hemispherical dome is the total area occupied by the boundary or surface of the dome.
It is measured in square units. A hemispherical dome is a 3D shape that resembles half of a sphere with a circular base.
It has a curved top and a flat base, so it has two surface areas: the curved surface area and the total surface area.
Surface Area of a Hemispherical Dome Formula
A hemispherical dome has a curved surface, and it has two types of surface areas: the curved surface area and the total surface area.
Look at the hemispherical dome below to see its surface area and radius(r).
A hemispherical dome has two types of surface areas: Curved Surface Area of a Hemispherical Dome Total Surface Area of a Hemispherical Dome
Curved Surface Area of a Hemispherical Dome
The area of the curved part of the dome, excluding its base, is known as the curved surface area of a hemispherical dome.
The formula for the curved surface area (CSA) of the dome is given as: Curved Surface Area = 2πr² square units
Here, r is the radius of the base of the dome.
Total Surface Area of a Hemispherical Dome
The total area occupied by the dome, including the area of the curved surface and the area of the circular base, is known as the total surface area of the hemispherical dome.
The total surface area of the dome is calculated by using the formula: Total Surface Area = 3πr² square units Where r is the radius of the base of the dome.
Derivation of the Total Surface Area of a Hemispherical Dome To find the total surface area of a hemispherical dome, consider the curved surface area and the base area.
Total Surface Area of a Hemispherical Dome = Base Area of a Hemispherical Dome + Curved Surface Area of a Hemispherical Dome
Here, the base area of a hemispherical dome = πr²
Curved surface area of a hemispherical dome = 2πr²
Substituting the formulas into the total surface area,
Total surface area of a hemispherical dome, T = πr² + 2πr²
Therefore, the total surface area of the hemispherical dome T = 3πr²
Volume of a Hemispherical Dome
The volume of a hemispherical dome shows how much space is inside it. It tells us how much space is inside the dome or how much it can hold.
The volume of a hemispherical dome can be found by using the formula: Volume = ⅔ (πr³) (cubic units)
Confusion between CSA and TSA
Students assume that the curved surface area (CSA) and the total surface area (TSA) of a hemispherical dome are the same.
This confusion arises because both involve the radius.
Always remember that CSA is used for only the curved part of the dome, and TSA includes the curved surface and the base.
Mistake 1
Using the wrong formula for surface area
Some students mistakenly use the formula for the surface area of a sphere instead of a hemispherical dome. Remember the formula for the total surface area of a hemispherical dome is 3πr².
Mistake 2
Using the wrong value for π
A common mistake of students is using 22 as the value of π. Instead, use accurate values like 22/7 or 3.14. π is a special number in math, and using the correct value is important for getting the right answer.
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 hemispherical dome, they mean the same thing. So, use the same formula for both.
Mistake 5
Solved Examples of Surface Area of Hemispherical Dome
Find the curved surface area of a hemispherical dome with a radius of 7 cm.
CSA = 308 cm²
Problem 1
Given r = 7 cm. Use the formula: CSA = 2πr² = 2 × (22/7) × 7 × 7 = 2 × 22 × 7 = 308 cm²
Find the total surface area of a hemispherical dome with a radius of 5 cm.
Explanation
TSA = 235.5 cm²
Problem 2
Use the formula: TSA = 3πr² = 3 × 3.14 × 5 × 5 = 3 × 3.14 × 25 = 235.5 cm²
A hemispherical dome has a radius of 6 cm. Find the total surface area.
Explanation
TSA = 339.12 cm²
Problem 3
Use the TSA formula: TSA = 3πr² = 3 × 3.14 × 6 × 6 = 3 × 3.14 × 36 = 339.12 cm²
Find the curved surface area of a hemispherical dome with a radius of 3.5 cm.
Explanation
CSA = 77 cm²
Problem 4
CSA = 2πr² = 2 × (22/7) × 3.5 × 3.5 = 22 × 1 × 3.5 = 77 cm²
The total surface area of a hemispherical dome is 462 cm². Find the radius.
Explanation
Radius = 7 cm
It is the total area that covers the outside of the hemispherical dome, including its curved part and the base.
1.What are the two types of surface area in a hemispherical dome?
2.What is the difference between curved surface area and 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 Hemispherical Dome
Students often make mistakes while calculating the surface area of a hemispherical dome, which leads to wrong answers. Below are some common mistakes and the ways to avoid them.
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Seyed Ali Fathima S
About the Author
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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