November 19, 2019, 06:27:02 AM
Forum Rules: Read This Before Posting


Topic: Volume of a sphere as a function of its depth  (Read 34601 times)

0 Members and 1 Guest are viewing this topic.

Offline billnotgatez

  • Global Moderator
  • Sr. Member
  • ***
  • Posts: 3838
  • Mole Snacks: +212/-55
  • Gender: Male
Re: Volume of a sphere as a function of its depth
« Reply #30 on: May 10, 2006, 06:15:05 PM »
I assume everyone has done integration of a quarter of a unit circle to get ¼ pi. Why not do something similar with a sphere?

Offline xiankai

  • Chemist
  • Full Member
  • *
  • Posts: 786
  • Mole Snacks: +77/-37
  • Gender: Male
Re: Volume of a sphere as a function of its depth
« Reply #31 on: May 12, 2006, 12:34:08 AM »
ok so far i've learnt that the general equation of a circle is x2 + y2 = r2,

and that integration of a sphere involves squaring the function and multiplying it by pi.

didnt know that in the first place  :o

(h - ro)2

umm... why do u subtract the radius of the sphere from the depth... isnt that akin to finding the upper half of the sphere?

while your method works; i've tried it already, i dont understand the above part :(

PS: snacks for everyone by the way, cheers :D
one learns best by teaching

Offline Donaldson Tan

  • Editor, New Asia Republic
  • Retired Staff
  • Sr. Member
  • *
  • Posts: 3178
  • Mole Snacks: +261/-12
  • Gender: Male
    • New Asia Republic
Re: Volume of a sphere as a function of its depth
« Reply #32 on: May 12, 2006, 02:43:41 PM »
1. cut the sphere into 2 and u see a circle.

2. put that circle on a graph paper, such that the y-axis is the depth of water, and the x-axis is the radius of the cross section.

3. you end up with a circle of origin (0,ro)

4. the general formula of a circle is (x - a)2 + (y - b)2 = R2 where (a,b) is the centre and R is the radius of the circle.

5. Hence, I use the formula (h - ro)2 + r2 = ro2

"Say you're in a [chemical] plant and there's a snake on the floor. What are you going to do? Call a consultant? Get a meeting together to talk about which color is the snake? Employees should do one thing: walk over there and you step on the friggin� snake." - Jean-Pierre Garnier, CEO of Glaxosmithkline, June 2006

Offline Donaldson Tan

  • Editor, New Asia Republic
  • Retired Staff
  • Sr. Member
  • *
  • Posts: 3178
  • Mole Snacks: +261/-12
  • Gender: Male
    • New Asia Republic
Re: Volume of a sphere as a function of its depth
« Reply #33 on: May 12, 2006, 02:53:11 PM »
umm... why do u subtract the radius of the sphere from the depth... isnt that akin to finding the upper half of the sphere?

See the graph above and see for yourself what I am actually doing.

the function of the volume of water as a function of height is thus:
volume of water = pi.f(h) = pi (roh2 -  h3/3 )

Cheers for the scooby snacks btw.

« Last Edit: May 12, 2006, 02:55:51 PM by geodome »
"Say you're in a [chemical] plant and there's a snake on the floor. What are you going to do? Call a consultant? Get a meeting together to talk about which color is the snake? Employees should do one thing: walk over there and you step on the friggin� snake." - Jean-Pierre Garnier, CEO of Glaxosmithkline, June 2006

Offline xiankai

  • Chemist
  • Full Member
  • *
  • Posts: 786
  • Mole Snacks: +77/-37
  • Gender: Male
Re: Volume of a sphere as a function of its depth
« Reply #34 on: May 12, 2006, 10:09:43 PM »
ok i understand everything now... thanks guys!
one learns best by teaching

Offline xiankai

  • Chemist
  • Full Member
  • *
  • Posts: 786
  • Mole Snacks: +77/-37
  • Gender: Male
Re: Volume of a sphere as a function of its depth
« Reply #35 on: May 25, 2006, 10:06:01 AM »
ok i still have some questions;

i realised that if we looked at the area of a circle as a line, we can then treat it as a diameter; finding the area of the new circle with this new diameter should give the volume of the sphere from what i visualise.

however, the main catch is that instead of ?(A/2)2, the method outlined above involves  ?(A)2.

can anyone explain this discrepancy? :)
one learns best by teaching

Sponsored Links