### 3-D Geometry

Posted:

**Mon Mar 10, 2008 7:41 am**Hi

Can anyone help me with this.

Regards

PS:PLEASE DO PROVIDE THE WAY TO WORK UP TO ANSWER.

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?

Can anyone help me with this.

Regards

PS:PLEASE DO PROVIDE THE WAY TO WORK UP TO ANSWER.

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?