Calculating Volume of a Football Using Integration | Step-by-Step Guide

[charlie95]

How to find the volume?

If we have a footbal, let us say that the radius is 1meter, how do we calculate the volume ??
And show it with Integral! (V= ∫∫∫dxdydz )

 

[jtbell]

American football or rest-of-the-world football?

First, you try to set up the integral, and then we can help you improve it if it's wrong. We don't give direct answers to things like this here, but we'll try to steer you in the right direction towards the answer.

 

[charlie95]

haha... funny guy :D rest-of the-world football!
If we have a huge footbal with radius of 1 meter. How could I find the volume of that ball without using a formulae book...

 

[russ_watters]

As jtbell said, we require that you first make an effort to solve it yourself and then we'll help you if you've done it wrong.

 

[Integral]

For any real football anything you can do mathematically will be at best a rough approximation. Unless you can come up with a precise mathematical expression. Footballs are roughly ellipsoid, however getting an exact expression may not be possible.

The best way to find the volume of a real object is not mathematically, but just dunk it in a container of water and measure the volume or mass of the displaced water.

 

[charlie95]

just forget it. I was just interested to know how we can do this mathematically with integral. I don't care if it is a football/baskeball/tennsball or etc.. Just that it is round(sphere) and has a radius of 1 meter.. the radius is not that important either, it can be 1000000000000 meters... I am just interested to find out how we can calculate it mathematically... And this is not a task that I have been given...

I understand that russ watters. But i am not sure where to begin..
V=∫∫∫r dxdydz...
.

 

[K^2]

Well, formally, you have $\displaystyle \iiint_{x^2+y^2+z^2<R^2}dx dy dz$. But that's not terribly helpful, because the integral boundary is inconvenient. Consider switching to polar coordinates. What are the dx, dy, and dz equal to in terms of dr, dθ, and dφ?

 

[jtbell]

i am not sure where to begin...

Google might be of some help. Seriously! In the eight hours since your first post in this thread, you probably could have found many web pages that discuss finding the volume of a sphere via integration. (Yes, I've looked, myself, to make sure of this.)

If you have trouble understanding them, choose one, give us a link, and tell us what you don't understand about it. Then we'll have something specific to help you with.

 

[charlie95]

I have a life jtbell...thanks for nothing...
I found many web pages, but many of them do it differently.thanks k^2... I solved the problem... much easier swithing over to polar coordinates.