The image above represents a segment of a sphere.

To compute the centre of gravity of a segment of a sphere requires two essential parameters. These parameters are the **radius of the sphere** and **height of the segment of the sphere**.

The formula for computing the centre of gravity of a sphere is:

C.G. = ^{3(2r – h)²} / _{4(3r – h)}

Where:

C.G. = Centre of Gravity

r = Radius of the Sphere

h = Height of the Segment of the Sphere

Let’s solve an example

Find the centre of gravity of the segment of the sphere where the radius of the sphere is 10 m and the height of the segment of the sphere is 4 m.

This implies that:

r = Radius of the Sphere = 10

h = Height of the Segment of the Sphere = 4

C.G. = ^{3(2(10) – 4)²} / _{4(3(10) – 4)}

C.G. = ^{3(20 – 4)²} / _{4(30 – 4)}

C.G. = ^{3(16)²} / _{4(26)}

C.G. = ^{3(256)} / _{104}

C.G. = ^{768} / _{104}

C.G. = 7.38

Therefore, the **centre of gravity of the segment of the sphere** is **7.38**.

Nickzom Calculator – **The Calculator Encyclopedia** is capable of calculating the centre of gravity of a segment of a sphere at a height, h at a distance from the centre of the sphere measured along the height.

Continue reading How to Calculate and Solve the Centre of Gravity of a Segment of a Sphere