Volume of a sphere by circle-areas

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SUMMARY

The volume of a sphere can be calculated by summing the volumes of horizontal disks rather than using the shell method. This approach involves integrating the areas of these disks, each with a thickness of Δy. It is essential to understand that while areas can be summed, only increments of volume should be summed to achieve the total volume of the sphere.

PREREQUISITES
  • Understanding of integral calculus
  • Familiarity with the concept of volume and area
  • Knowledge of the shell method in calculus
  • Basic understanding of horizontal cross-sections
NEXT STEPS
  • Study the method of integrating horizontal disks for volume calculation
  • Explore the shell method in detail for comparative analysis
  • Learn about the applications of volume integration in physics
  • Investigate the relationship between area and volume in higher dimensions
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Students and educators in mathematics, particularly those focusing on calculus, as well as professionals in fields requiring geometric volume calculations.

Nikitin
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Instead of the shell method, can't one find the volume of a sphere by integrating/summing its horizontal areas?
 
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Nikitin said:
Instead of the shell method, can't one find the volume of a sphere by integrating/summing its horizontal areas?
Sure, if you mean using horizontal disks of thickness Δy. You can't sum areas to get a volume. You can sum increments of volume to get a total volume.
 

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