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

Last Updated on February 14, 2024

The image above represents a segment of a sphere.
To compute the center 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)}
So, C.G. = ^3(16)² / ₄₍₂₆₎
C.G. = ³⁽²⁵⁶⁾ / ₁₀₄
C.G. = ⁷⁶⁸ / ₁₀₄
That is, C.G. = 7.38

Therefore, the center of gravity of the segment of the sphere is 7.38.

How to Calculate and Solve the Centre of Gravity of a Segment of a Sphere Using Nickzom Calculator

Nickzom Calculator – The Calculator Encyclopedia is capable of calculating the center 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.

To get the answer and workings of the center of gravity of a segment of a sphere using the Nickzom Calculator – The Calculator Encyclopedia. First, you need to obtain the app.

You can get this app via any of these means:

Web – https://www.nickzom.org/calculator-plus

To get access to the professional version via web, you need to register and subscribe for NGN 1,500 per annum to have utter access to all functionalities.
You can also try the demo version via https://www.nickzom.org/calculator

Android (Paid) – https://play.google.com/store/apps/details?id=org.nickzom.nickzomcalculator
Android (Free) – https://play.google.com/store/apps/details?id=com.nickzom.nickzomcalculator
Apple (Paid) – https://itunes.apple.com/us/app/nickzom-calculator/id1331162702?mt=8

Once, you have obtained the calculator encyclopedia app, proceed to the Calculator Map, then click on Mechanics under the Engineering section

Now, click on Centre of Gravity under Statics

Now, click on Centre of Gravity of a Segment of a Sphere

The screenshot below displays the page or activity to enter your values, to get the answer for the centre of gravity of a segment of a sphere according to their respective parameters which are the radius of the sphere (r) and the height of the segment of the sphere (h).

Now, enter the values appropriately and accordingly for the parameters as required by the example above where the radius of the sphere is 10 and the height of the segment of the sphere is 4.

Finally, click on the Calculate button

As you can see from the screenshots above, Nickzom Calculator – The Calculator Encyclopedia solves for the centre of gravity of a segment of a sphere and presents the formula, workings and steps too.