and that's the hard way - I did it that way too.
So - Since the final answer didn't have radius in it, just 'h', that means you can pick a cylinder of any radius you like - as long as h=6
I'd try the cylinder where radius approaches zero.......
that means the bead's diameter approaches h
that means the cylinder and cap volumes approach zero
So you are left with the volume of a sphere -
V = 4/3 pi r^3: where r = h/2 = 3
V = 36 pi
proof your answer is correct......
another - I have a number in mind. It's either 1, 2, or 3. Guess my number - you can ask me one question and I'll answer it 'yes', 'no', or "I don't know"
(goal - find a question that gives you the right answer no matter which number I chose)