How to find which z-value to cut at to get the appropriate volume of a sphere

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Discussion Overview

The discussion revolves around determining the z-coordinates for making a horizontal cut on a unit sphere to achieve a specific volume of the sphere that is removed. The focus is on the mathematical approach to find these coordinates, particularly in the context of volume calculations and integration.

Discussion Character

  • Exploratory, Mathematical reasoning

Main Points Raised

  • One participant seeks to understand how to calculate the z-coordinates for a horizontal cut on a unit sphere to achieve a volume of (1/4)*(4/3)*pi.
  • Another participant inquires about the mathematical background of the original poster, suggesting that their level of knowledge may influence the discussion.
  • A follow-up question asks about the original poster's understanding of integrals, indicating a potential need for foundational knowledge in calculus to address the problem.

Areas of Agreement / Disagreement

The discussion does not present any consensus, as it primarily consists of questions regarding the original poster's background and understanding rather than direct solutions or methods to find the z-coordinates.

Pixel08
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Hi PF!

I've been trying to find out how one could find which z-coordinates to 'cut' at to get a specific volume of the sphere cut off.

i.e. I have a unit sphere, therefore the total volume is (4/3)*pi*r^3, where r = 1. Now I want to get 1/4 of that volume cut off. So, (1/4)*(4/3)*pi*r^3.

But the problem is, how do I find out where I made that single cut? (The cut has to be horizontal).
 
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What is your mathematics background?
 
DivisionByZro said:
What is your mathematics background?

Hi DivisionByZro! I'm a first year student, just started post-secondary. Not much of a mathematics background - took a differential calculus course last term.
 
What do you know about integrals?
 

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