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
Messages
3
Reaction score
0
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).
 
Mathematics news on Phys.org
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?
 
Thread 'Video on imaginary numbers and some queries'

Thread 'Video on imaginary numbers and some queries'

Hi, I was watching the following video. I found some points confusing. Could you please help me to understand the gaps? Thanks, in advance! Question 1: Around 4:22, the video says the following. So for those mathematicians, negative numbers didn't exist. You could subtract, that is find the difference between two positive quantities, but you couldn't have a negative answer or negative coefficients. Mathematicians were so averse to negative numbers that there was no single quadratic...
View full post »

Thread 'What Exactly is Dirac’s Delta Function? - Insight'

Insights auto threads is broken atm, so I'm manually creating these for new Insight articles. In Dirac’s Principles of Quantum Mechanics published in 1930 he introduced a “convenient notation” he referred to as a “delta function” which he treated as a continuum analog to the discrete Kronecker delta. The Kronecker delta is simply the indexed components of the identity operator in matrix algebra Source: https://www.physicsforums.com/insights/what-exactly-is-diracs-delta-function/ by...
View full post »
Thread 'Unit Circle Double Angle Derivations'

Thread 'Unit Circle Double Angle Derivations'

Here I made a terrible mistake of assuming this to be an equilateral triangle and set 2sinx=1 => x=pi/6. Although this did derive the double angle formulas it also led into a terrible mess trying to find all the combinations of sides. I must have been tired and just assumed 6x=180 and 2sinx=1. By that time, I was so mindset that I nearly scolded a person for even saying 90-x. I wonder if this is a case of biased observation that seeks to dis credit me like Jesus of Nazareth since in reality...
View full post »

Similar threads

I Higher Dimensional Spheres viz. Cubes
Replies
1
Views
1K
B A question about one of Archimedes' works
Replies
5
Views
2K
I Volumes of n-Spheres: Intuition & Calculations
Replies
8
Views
3K
B Question about volume of a sphere
Replies
16
Views
3K
A Finding Minimal Mean Distance Curves on the Unit Sphere
Replies
2
Views
2K
I What is the name of the software company behind the MSG Sphere in Las Vegas?
Replies
1
Views
2K
Finding Volumes of Sphere & Circular Cone: Alpha from 0 to Pi
Replies
3
Views
2K
Finding the Centre of Mass of a Hemisphere
Replies
13
Views
3K
B Invariant under rotation: Banal, obvious, or noteworthy?
Replies
2
Views
2K
MHB How Does Boyle's Law Explain the Pressure-Volume Relationship of CO2?
Replies
3
Views
3K

Hot Threads

Recent Insights

Back
Top