I did it 'lemonoman's way' (or the 'right' way!). I am not entirely sure what Vant_Hoff did, for some reason I got a different answer to him- probably me making some mistake somewhere in the calculation.
I used spherical coordinates instead of rectangular. Now sure you you went straight into numerical app and solved it . Try finding a general expression using rect coord, u'll see how much easier it is to apply spherical coordinates in this case. This is something known just as when you work with a cylinder , u use cylindrical coord.
lol , I hope I didn't offend Vant_Hoff- I think he has got the right idea of finding the volume of a sphere- but when you want to find the volume of part of a sphere, the best way to do it is by integrating, rather than trying to work out a fraction of the sphere. (Also, being Canadian, I am more likely to favour lemonoman over Vant_Hoff
No problem mate, I'm not offended at all
I use a proportional const only if I must and only when I'm sure of it. Ofcourse, in a general sense, it does not work.
That's were you have gone astray You are calculating not only volume of the portion of the sphere, but also volume of the cone attached to it and going down to the sphere centre.
I've edited my reply and corrected the variable p. When I thought about this problem, I assumed that the distance between the plane that cuts the sphere, say at z=h, and the center can be neglected, but since you've pointed out yesterday that your ans is different, I recheked it today with some app in the book. It turned out the difference can sometimes be large ( my ans was about 296 instead 309 ) , and so I plugged in the correct variable h/Cos(Phi).
You owe me ?2 snacks
If you say so , but still u didn't come up with any correction man!