Calculate Mass of Material for Hollow Spherical Shell

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Discussion Overview

The discussion revolves around calculating the mass of a hollow spherical shell given its inner and outer radii, as well as the material's density. The scope includes mathematical reasoning and conceptual clarification related to volume calculations.

Discussion Character

  • Mathematical reasoning, Conceptual clarification, Homework-related

Main Points Raised

  • One participant asks how to find the mass of a hollow spherical shell with specified inner and outer radii and density.
  • Another participant suggests calculating the volume of the shell by subtracting the volume of the inner sphere from the outer sphere and then multiplying by the density.
  • A participant questions the lack of numerical values for the radii, indicating confusion about the volume calculation.
  • Another participant asserts that the radii are symbolic representations, allowing for a general formula applicable to any specific values of r1 and r2.
  • A hint is provided regarding the formula for the volume of a sphere, reinforcing the need for understanding the volume calculation.

Areas of Agreement / Disagreement

Participants express confusion regarding the numerical values of the radii, and while some clarify the symbolic nature of r1 and r2, there is no consensus on the interpretation of the problem.

Contextual Notes

The discussion highlights the need for clarity on the use of symbolic representations in mathematical problems, as well as the assumptions involved in volume calculations.

rumaithya
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Hello,

How can we find the mass of a material with density p is required to make a hollow spherical shell having inner radius r1 and outer radius r2 ?

Thanks
 
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rumaithya said:
Hello,

How can we find the mass of a material with density p is required to make a hollow spherical shell having inner radius r1 and outer radius r2 ?

Thanks
Find the volume of the shell by taking the volume of a sphere or radius r2 and subtract out the volume of a sphere of radius r1. Then multiply the mass density times the volume.

Pete
 
What is the volume of r1 and r2 ?! there isn't any given numbers
 
Yes, there are! r1 and r2 are numbers.

The volume of the hollow shell is [itex]\frac{4\pi}{3} (r_1^3-r_2^3)[/itex]. Now multiply by ρ to get the mass.
 
rumaithya said:
What is the volume of r1 and r2 ?! there isn't any given numbers
Hint: The volume of a sphere of radius r is [itex]V = \frac{4}{3}\pi r^3[/itex].

Pete
 
you can think of r1 and r2 as just representations of numbers. It is a way of representing ANY number rather than one particular number. By doing this, if you have any sphere of any radius, you can just plug in the number you want to calculate in place of r1 and r2. This gives you a convienet equation that is applicable to any situation.
 

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