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

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SUMMARY

The discussion focuses on finding the center of mass of a half-ball, specifically a hemisphere. Zachary Lindsey seeks validation for his calculations and is advised that integration is unnecessary for determining the volume of the hemisphere, which is simply (1/2)(4π). The conversation emphasizes the importance of understanding geometric properties and volume calculations in physics and mathematics.

PREREQUISITES
  • Understanding of geometric properties of a hemisphere
  • Familiarity with volume calculations in calculus
  • Basic knowledge of integration techniques
  • Concept of center of mass in physics
NEXT STEPS
  • Study the geometric properties of three-dimensional shapes
  • Learn about volume calculations for various solids, including spheres and hemispheres
  • Explore the concept of center of mass in different coordinate systems
  • Review integration techniques relevant to finding volumes and centers of mass
USEFUL FOR

Students in physics and mathematics, educators teaching geometry and calculus, and anyone interested in understanding the principles of center of mass and volume calculations.

CaptainZappo
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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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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\pi)!)
 

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