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

AI Thread Summary
To determine the z-coordinate for cutting a unit sphere to achieve a specific volume, one must use the formula for the volume of a sphere, which is (4/3)πr³. For a unit sphere, the total volume is (4/3)π. To find the z-coordinate that results in cutting off 1/4 of this volume, the volume of the cut section needs to be calculated as (1/4)(4/3)π. The discussion highlights the need for understanding integrals to solve this problem, as integrating the volume of the sphere from the top down to the desired z-coordinate will yield the necessary cut location. A foundational knowledge of calculus, particularly integrals, is essential for solving this type of volume problem.
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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