What Is a Hemisphere?

Before we dive into calculations, let's make sure we understand our shapes.

Hemisphere

A hemisphere is exactly half of a sphere, created by cutting a sphere along a flat plane through its centre. It has one curved surface and one flat circular face (the "base").

Think of slicing an orange perfectly in half — each piece is a hemisphere. A bowl, a dome on a building, or half a basketball are all real-world examples of hemispheres.

Every hemisphere is defined by a single measurement: the radius ( $r$ ), which is the same as the radius of the original sphere it came from.

Volume of a Hemisphere

Since a hemisphere is exactly half of a sphere, we start with the volume of a sphere and divide by two.

The volume of a sphere is:
$V_{sphere} = \frac{4}{3} π r^{3}$

So the volume of a hemisphere is:
$V_{hemisphere} = \frac{1}{2} \times \frac{4}{3} π r^{3} = \frac{2}{3} π r^{3}$

Exam Tip

Remember: volume tells us how much space is inside a 3D shape. It's measured in cubic units (cm³, m³, etc.).

Example

Find the volume of a hemisphere with radius 6 cm.

$V = \frac{2}{3} π r^{3}$
$V = \frac{2}{3} \times π \times 6^{3}$
$V = \frac{2}{3} \times π \times 216$
$V = 144 π$
$V \approx 452.4 cm^{3}$

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