Volume

rcarlton88 · February 3rd, 2008, 8:01 pm

The surface y^2 + z^2 =1 in 3-space is an example of an (infinite) horizontal right circular cylinder of radius 1; the axis of this particular cylinder is the x-axis. Now suppose we have n horizontal right circular cylinders, all of radius 1, whose axes are all (horizontal) lines through the origin which make equal angles to each other there. (For instance , if n=4, the axes could be the x- and y-axes and the lines y=x and y=-x.) a. Find the volume that lies within all n cylinders.b. What happens to your answer from a) as n->infinity? Can you explain this?

VCA · February 4th, 2008, 7:07 pm

Vassili · February 4th, 2008, 7:56 pm

It has been answered already at this post. When n->infinity, shouldn't the shape become the unit sphere?

rcarlton88 · February 6th, 2008, 2:35 pm

The answer that the guy gave was for 2 cylinders. The answer should have an n in it.

Tschortscho · February 17th, 2008, 9:56 pm

Tried this yesterday and obtained the following answer to question (a): . For n=2 this gives the same result as in the post mentioned above; for n -> infinity it yields the volume of the unit ball.