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

Pixel08

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).

DivisionByZro

What is your mathematics background?

Pixel08

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.

DivisionByZro

What do you know about integrals?