How to Find the Center of Mass of a Half-Ball?

In summary, Zachary has been working on a question and has asked for someone to check for any errors. He has attached a scanned copy of the question and his work. The other person responds that they do not see any errors, but notes that integrating is not necessary to find the volume of a hemisphere.
  • #1
CaptainZappo
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0
Hi, I've been working on the following question for a little while. I've looked it over several times and I can't find any obvious (to me anyway) errors in my work. Would you please scan it through and let me know if I am correct or, if not, please guide me in the right direction so I can try again.

I have attached a scanned copy of the question and my work.

Thank you in advance,
-Zachary Lindsey
 

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  • #2
I don't see anything wrong with it.

(Except that you really don't need to integrate to find the volume of the hemisphere: it is (1/2)(4[itex]\pi[/itex])!)
 

Related to How to Find the Center of Mass of a Half-Ball?

What is the center of mass of a half-ball?

The center of mass of a half-ball is the point at which the mass of the half-ball is evenly distributed in all directions.

How is the center of mass of a half-ball calculated?

The center of mass of a half-ball can be calculated by finding the average of the x, y, and z coordinates of each point on the surface of the half-ball.

Does the shape of the half-ball affect its center of mass?

Yes, the shape of the half-ball affects its center of mass. The center of mass will be closer to the flat side of the half-ball and further from the curved side.

What is the significance of the center of mass of a half-ball?

The center of mass of a half-ball is important in understanding the stability and balance of the object. It is also used in calculations involving rotational motion and collisions.

How can the center of mass of a half-ball be used in real-world applications?

The center of mass of a half-ball can be used in designing structures, such as domes and arches, to ensure stability and balance. It is also important in sports, such as bowling and golf, to determine the path and speed of the ball.

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