Understanding Inner and Outer Radius

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SUMMARY

The discussion focuses on calculating the mass of a hollow spherical shell with an inner radius (r1) and an outer radius (r2) using the density (p) of the material. To find the mass, one must first determine the volume of the shell by subtracting the volume of the inner sphere (radius r1) from the volume of the outer sphere (radius r2). The formula for the volume of a sphere, V = (4/3)πr³, is applied to both radii, and the difference provides the volume of the shell. Subsequently, the mass can be calculated using the formula mass = density × volume.

PREREQUISITES
  • Understanding of basic geometry, specifically the volume of spheres.
  • Familiarity with the concept of density and its formula.
  • Knowledge of mathematical operations involving subtraction and multiplication.
  • Basic grasp of physics principles related to mass and volume.
NEXT STEPS
  • Study the formula for the volume of a sphere: V = (4/3)πr³.
  • Learn about density and its applications in physics.
  • Explore problems involving hollow objects in physics to enhance understanding.
  • Investigate the relationship between mass, volume, and density in different materials.
USEFUL FOR

This discussion is beneficial for students preparing for physics courses, particularly those studying concepts related to geometry, mass, and density in hollow objects. It is also useful for educators looking to clarify these concepts for their students.

mysticxhobo
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Im new to these forums and I'm looking forward to becoming a regular contributor. I'm attempting to prepare for physics in the fall and I have a textbook problem that i understand the process of solving but not understand the concept.

Heres the question:
What mass of a material w/ density p is required to make a hollow spherical shell having inner radius r1 and outer radius r2?

I understand everything besides the inner and outer radius part. What is the textbook trying to say with that statement. How do you know to subtract them? So if you understood to subtract the radii can you please explain your thought process?

Again thanks a a lot.
 
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'Hollow' means 'It ain't dere no mo.'

If I have a 'hollow spherical shell', it means the outer surface of the sphere has a radius 'r2' for instance and the inside surface of the hollow spherical shell, which isn't there, has a radius of 'r1' for instance.
 
The difference between the two radii is the thickness of the shell. You can determine the volume of the shell by subtracting the volume of a sphere of radius r1 from the volume of a sphere of radius r2. Once you know the volume of the shell, you can calculate its mass with a given density or vice-versa.
 

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