Surface Area of Hollow Hemisphere
2026-02-28 17:12 Diff
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Last updated on August 30, 2025

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.

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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).

Problem 1

Given R = 7 cm. Use the formula: Outer CSA = 2πR² = 2 × (22/7) × 7 × 7 = 2 × 22 × 7 = 308 cm²

Okay, lets begin

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

Well explained 👍

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

Okay, lets begin

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

Well explained 👍

Problem 3

Use the formula: Inner CSA = 2πr² = 2 × 3.14 × 3 × 3 = 2 × 3.14 × 9 = 6.28 × 9 = 56.52 cm²

Okay, lets begin

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

Well explained 👍

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

Okay, lets begin

The outer curved surface area of a hollow hemisphere is 200 cm². Find the outer radius.

Explanation

Outer Radius = 5.64 cm

Well explained 👍

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?

Outer curved surface area and inner curved surface area are the two types of surface areas in a hollow hemisphere.

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

The outer radius is the radius of the outer surface, while the inner radius is the radius of the inner surface.

3.Is curved surface area the same as lateral surface area?

Yes, in hollow hemispheres, both curved and lateral surface area mean the same.

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 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.

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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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