105 LearnersLast updated on August 30, 2025
Surface Area of Hollow Sphere
A hollow sphere is a 3-dimensional shape that consists of two concentric spherical surfaces: an outer surface and an inner surface. The surface area of a hollow sphere is the total area covered by its outer and inner surfaces. In this article, we will learn about the surface area of a hollow sphere.
What is the Surface Area of a Hollow Sphere?
The surface area of a hollow sphere is the total area occupied by the boundary or surface of both the outer and inner spheres.
It is measured in square units.
A hollow sphere consists of two concentric spheres—an inner sphere and an outer sphere.
The surface area of a hollow sphere is the sum of the surface areas of these two spheres.
Surface Area of a Hollow Sphere Formula
A hollow sphere has two surfaces: the outer surface and the inner surface.
The total surface area is the sum of the areas of these surfaces.
Consider a hollow sphere with an outer radius R and an inner radius r.
Surface Area of a Hollow Sphere = Outer Surface Area + Inner Surface Area
Outer Surface Area of a Hollow Sphere
The outer surface area of a hollow sphere is the area of the external spherical surface.
The formula for the outer surface area of the hollow sphere is given as:
Outer Surface Area = 4πR² square units
Here, R is the outer radius of the hollow sphere.
Inner Surface Area of a Hollow Sphere
The inner surface area of a hollow sphere is the area of the internal spherical surface.
The formula for the inner surface area of the hollow sphere is:
Inner Surface Area = 4πr² square units
Where r is the inner radius of the hollow sphere.
Total Surface Area of a Hollow Sphere
The total surface area of a hollow sphere is calculated by summing the outer and inner surface areas:
Total Surface Area = 4πR² + 4πr² = 4π(R² + r²) square units
This formula considers both the inner and outer surfaces of the hollow sphere.
Volume of a Hollow Sphere
The volume of a hollow sphere is the volume enclosed between the two concentric spheres. It is calculated as the difference between the volumes of the outer sphere and the inner sphere.
The volume formula is: Volume = ⅔π(R³ - r³) cubic units
Confusion between Outer and Inner Surface Areas
Students sometimes confuse the outer surface area with the inner surface area.
Always remember to use the outer radius R for the outer surface area and the inner radius r for the inner surface area.
Mistake 1
Using Diameter Instead of Radius
Some students mistakenly use the diameter instead of the radius. Remember that the formulas for surface areas use the radius, not the diameter.
Mistake 2
Using the Wrong Value for π
A common error is using incorrect values for π. Always use accurate values like 22/7 or 3.14 for π to ensure accurate calculations.
Mistake 3
Forgetting to Add Both Surface Areas
Students might calculate only one surface area and forget to sum both the outer and inner surface areas. Ensure to add both to find the total surface area.
Mistake 4
Assuming Surface Area and Volume Are the Same
Surface area and volume are different measurements. Surface area is the total area of the surfaces, while volume measures the space enclosed. Do not confuse these two concepts.
Mistake 5
Solved Examples of Surface Area of Hollow Sphere
Find the outer surface area of a hollow sphere with an outer radius of 10 cm.
Outer Surface Area = 1256 cm²
Problem 1
Given R = 10 cm. Use the formula: Outer Surface Area = 4πR² = 4 × 3.14 × 10² = 4 × 3.14 × 100 = 1256 cm²
Find the total surface area of a hollow sphere with outer radius 8 cm and inner radius 5 cm.
Explanation
Total Surface Area = 1318.4 cm²
Problem 2
Use the formula: Total Surface Area = 4π(R² + r²) = 4 × 3.14 × (8² + 5²) = 4 × 3.14 × (64 + 25) = 4 × 3.14 × 89 = 1318.4 cm²
A hollow sphere has an outer radius of 12 cm and an inner radius of 9 cm. Find its inner surface area.
Explanation
Inner Surface Area = 1017.36 cm²
Problem 3
Use the formula: Inner Surface Area = 4πr² = 4 × 3.14 × 9² = 4 × 3.14 × 81 = 1017.36 cm²
Find the total surface area of a hollow sphere with outer radius 7 cm and inner radius 4 cm.
Explanation
Total Surface Area = 968 cm²
Problem 4
Total Surface Area = 4π(R² + r²) = 4 × 3.14 × (7² + 4²) = 4 × 3.14 × (49 + 16) = 4 × 3.14 × 65 = 968 cm²
The inner surface area of a hollow sphere is 452.16 cm². Find the inner radius.
Explanation
Inner Radius = 6 cm
It is the total area that covers the outer and inner surfaces of the hollow sphere.
1.What are the two types of surface areas in a hollow sphere?
2.What is the difference between outer radius and inner radius?
3.Is the surface area the same as the volume?
4.What unit is surface area measured in?
Common Mistakes and How to Avoid Them in the Surface Area of a Hollow Sphere
Students often make mistakes while calculating the surface area of a hollow sphere, which leads to incorrect 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
