Cutting a hollow sphere into 2 piece but not in half

[athrun200]

Homework Statement

A uniform sphere of radius R is cut into two portions. The smaller portion S has height h measured from its flat surface, where h<R.

(a) Locate the center of mass of S from its flat surface

(b) Use (a) the locate the centre of mass of a hollow H which has the same shape and same size as S. The hollow has only a thin curved surface and without any flat surface.
(c) Obtain the result of (b) by direct integration.

Homework Equations

This question use 2 tricks to find the center of mass of a hollow.
1. Use substraction to substract a big object by a smaller one and then take limit. (I hope you understand what I mean.)
2. Use direction integration.

The Attempt at a Solution

My answer in part b doesn't agree with part c, can anyone help me to check what happen?

 

[vela]

I found a different expression for the mass of the cap:
m=\frac{\rho\pi h^2(3R-h)}{3}

 

[athrun200]

I found a different expression for the mass of the cap:
m=\frac{\rho\pi h^2(3R-h)}{3}

In fact I have same expression as you
\frac{h^{3}}{3}-h^{2}R

But when I copy it form messy worksheet to a much neat writting, I try to simplfy the expression in my mind, unforunately, I fail

So my expression for the mass is also correct.

 

[vela]

Did you get it to work out?

 

[athrun200]

Did you get it to work out?

Yes, of course.
I do this question with 2 other classmates, we check a hundred time for our answer. I am sure we get it correct.

 

[tim94131358]

so may i ask for b) and c)

the ans is..h/2 or h(4R-4) / 3(3R-h)

cuz my ans is not same as yours...

btw where the ans for b and c are not the same

 

[vela]

The answers you get for b and c should both be h/2.

 

[athrun200]

so may i ask for b) and c)

the ans is..h/2 or h(4R-4) / 3(3R-h)

cuz my ans is not same as yours...

btw where the ans for b and c are not the same

what do you get?