Surface-image from mathematica.

[ladybeetle]

Homework Statement

Find the parametric equations in the surface S therefore
Z^2=1+x^2+y^2 and 2 ≤z ≤3
and draw the image of the surface with Mathematica

Homework Equations

(below 3.)

The Attempt at a Solution

Use polar coordinates as parameters. The surface defined is part of a hyperboloid of two sheets. The condition 2 ≤ z ≤ 3 translates to 1 ≤ x² + y² ≤ 2 directly from the equation.

So let x = r cosΘ and y = r sinΘ where 1 ≤ r ≤ √(2) and 0 ≤ Θ ≤ 2π. Then z = √(1 + r²). Express this as the vector valued function

F(r, Θ) = r cosΘ i + r sinΘ j + √(1 + r²) k, 1 ≤ r ≤ √(2), 0 ≤ Θ ≤ 2π.

I don't know how to use Mathematica to draw the surface.
can anyone help me with it? I need a image of the surface from Mathematica.

 

[sunjin09]

surface image