help with helix x y crosssection

Here is the Question:

The parametric questions of a certain helix are

x=3cos(2*pi*t)
y=3sin(2*pi*t)
z=2t

what is the area of this helix xy-crosssection? what is the helix pitch?

how do i go about answering this using matlab? i graphed it with this code

t=-10:.01:10;
x=3*cos(2*pi*t);
y=3*sin(2*pi*t);
z=2*t;
plot3(x,y,z)

but how would i go about find the area and pitch?

thank you for your time

Answer 1

[Image Analyst]

I don't know what you mean by area since it's just a spiral going up the z axis, but x goes from -3 to +3 and so does y. So it's circular with a radius of 3 so the "area" if you look at it top down, along the z axis, is pi*3^2 = 28.2743338823081.

To get the pitch, first get the period. x gets back to the same x after t = 1, 2, 3, 4, etc. - basically integers because that is when 2*pi*t is a multiple of 2*pi. So when t = 1,2,3,4 then z will equal 2,4,6,8,.... So the period is 2 units of z which means the pitch is 1/2 unit of z^(-1).