Surface Area of Hollow Sphere
2026-02-28 23:12 Diff
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Last updated on August 30, 2025

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.

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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.

Problem 1

Given R = 10 cm. Use the formula: Outer Surface Area = 4πR² = 4 × 3.14 × 10² = 4 × 3.14 × 100 = 1256 cm²

Okay, lets begin

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

Well explained 👍

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

Okay, lets begin

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

Well explained 👍

Problem 3

Use the formula: Inner Surface Area = 4πr² = 4 × 3.14 × 9² = 4 × 3.14 × 81 = 1017.36 cm²

Okay, lets begin

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

Well explained 👍

Problem 4

Total Surface Area = 4π(R² + r²) = 4 × 3.14 × (7² + 4²) = 4 × 3.14 × (49 + 16) = 4 × 3.14 × 65 = 968 cm²

Okay, lets begin

The inner surface area of a hollow sphere is 452.16 cm². Find the inner radius.

Explanation

Inner Radius = 6 cm

Well explained 👍

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?

The two types of surface areas are the outer surface area and the inner surface area.

2.What is the difference between outer radius and inner radius?

The outer radius is the radius of the external sphere, while the inner radius is the radius of the internal sphere.

3.Is the surface area the same as the volume?

No, surface area is the total area of the surfaces, while volume measures the space enclosed.

4.What unit is surface area measured in?

Surface area is always measured in square units like cm², m², or in².

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.

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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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