102 LearnersLast updated on August 30, 2025
Surface Area of Hollow Hemisphere
A hollow hemisphere is a 3-dimensional shape that has a circular opening. The surface area of the hollow hemisphere is the total area covered by its outer and inner surfaces. The surface area of a hollow hemisphere includes both its curved outer surface and its curved inner surface, excluding the base. In this article, we will learn about the surface area of a hollow hemisphere.
What is the Surface Area of a Hollow Hemisphere?
The surface area of a hollow hemisphere is the total area occupied by the boundary or surface of a hollow hemisphere. It is measured in square units.
A hollow hemisphere is a 3D shape that looks like a half-sphere with an opening at the bottom.
It has a curved outer surface and a curved inner surface but no base, so it has two surface areas: the outer curved surface area and the inner curved surface area.
Surface Area of a Hollow Hemisphere Formula
A hollow hemisphere has both an outer and inner curved surface, and these contribute to its total surface area.
Look at the hollow hemisphere below to see its outer and inner surface areas, radius of the outer surface (R), and radius of the inner surface (r).
A hollow hemisphere has two types of surface areas: Outer Curved Surface Area of a Hollow Hemisphere Inner
Curved Surface Area of a Hollow Hemisphere
Outer Curved Surface Area of a Hollow Hemisphere
The area of the curved part of the outer surface is known as the outer curved surface area of a hollow hemisphere.
The formula for the outer curved surface area of the hollow hemisphere is given as:
Outer Curved Surface Area = 2πR² square units
Here, R is the radius of the outer surface of the hollow hemisphere.
Inner Curved Surface Area of a Hollow Hemisphere
The area of the curved part of the inner surface is known as the inner curved surface area of a hollow hemisphere.
The formula for the inner curved surface area of the hollow hemisphere is given as:
Inner Curved Surface Area = 2πr² square units
Here, r is the radius of the inner surface of the hollow hemisphere.
Total Surface Area of a Hollow Hemisphere
The total surface area occupied by the hollow hemisphere, including the outer and inner curved surfaces, is known as the total surface area of the hollow hemisphere.
The total surface area of a hollow hemisphere is calculated by using the formula:
Total Surface Area = 2π(R² + r²) square units
Where R is the radius of the outer surface, and r is the radius of the inner surface of the hollow hemisphere.
Confusion between inner and outer curved surface areas
Students assume that the inner and outer curved surface areas of a hollow hemisphere are the same.
This confusion arises because both involve the radius.
Always remember that the outer curved surface area uses the outer radius (R), and the inner curved surface area uses the inner radius (r).
Mistake 1
Using the same radius for both surfaces
Some students mistakenly use the same radius for calculating both the inner and outer curved surface areas. Remember that the outer curved surface area uses R, and the inner curved surface area uses r.
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 both curved surfaces in the total surface area
Students often calculate only one of the curved surfaces and forget to add the other. Always include both parts when calculating the total surface area. Total Surface Area = Outer Curved Surface Area + Inner Curved Surface 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 hollow hemisphere, they mean the same thing. So, use the same formula for both.
Mistake 5
Solved Examples of Surface Area of Hollow Hemisphere
Find the outer curved surface area of a hollow hemisphere with an outer radius of 7 cm.
Outer CSA = 308 cm²
Problem 1
Given R = 7 cm. Use the formula: Outer CSA = 2πR² = 2 × (22/7) × 7 × 7 = 2 × 22 × 7 = 308 cm²
Find the total surface area of a hollow hemisphere with outer radius 6 cm and inner radius 4 cm.
Explanation
Total Surface Area = 377.44 cm²
Problem 2
Use the formula: Total Surface Area = 2π(R² + r²) = 2 × 3.14 × (6² + 4²) = 2 × 3.14 × (36 + 16) = 2 × 3.14 × 52 = 6.28 × 52 = 377.44 cm²
A hollow hemisphere has an outer radius of 5 cm and an inner radius of 3 cm. Find the inner curved surface area.
Explanation
Inner CSA = 56.52 cm²
Problem 3
Use the formula: Inner CSA = 2πr² = 2 × 3.14 × 3 × 3 = 2 × 3.14 × 9 = 6.28 × 9 = 56.52 cm²
Find the total surface area of a hollow hemisphere with an outer radius of 8 cm and an inner radius of 6 cm.
Explanation
Total Surface Area = 659.52 cm²
Problem 4
Total Surface Area = 2π(R² + r²) = 2 × 3.14 × (8² + 6²) = 2 × 3.14 × (64 + 36) = 2 × 3.14 × 100 = 6.28 × 100 = 628 cm²
The outer curved surface area of a hollow hemisphere is 200 cm². Find the outer radius.
Explanation
Outer Radius = 5.64 cm
It is the total area that covers the outer and inner curved surfaces of the hollow hemisphere.
1.What are the types of surface area in a hollow hemisphere?
2.What is the difference between outer and inner radii?
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 Hollow Hemisphere
Students often make mistakes while calculating the surface area of a hollow hemisphere, which leads to wrong answers. Below are some common mistakes and the ways to avoid them.
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.
Fun Fact
: She has songs for each table which helps her to remember the tables
