# Homework Help: Parametric Equation of Surface [SOLVED]

1. Jul 19, 2015

### Phil Frehz

1. The problem statement, all variables and given/known data
Find parametric equations for the portion of the cylinder x2 + y2 = 5 that extends between the planes z = 0 and z=1.

2. Relevant equations
I can't really find any connection but I do have
x=a*sinv*cosu
y=a*sinv*sinu
z=a*cosv

3. The attempt at a solution

I understand that there is a cylinder of radius 5 between z=0 and z=1 however I don't understand how to translate it in terms of u & v. In polar coordinates I know r extends from the origin (r=0) to the cylindrical curve (r=1), while theta is from 0 to 2pi.

Attached is the solution, not sure how to connect the information together

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2. Jul 19, 2015

### Staff: Mentor

Just focusing on the circle in the x-y plane for the moment, think about how you would translate the circle's equation into polar coordinates. That should give you equations for x and y in terms of a parameter. The inequality for z is very simple, with v = z, but within a limited interval.

3. Jul 19, 2015

### Phil Frehz

Thanks for the input, I looked into it and found that v was the varying parameter, converting x and y to polar coordinates gave me the answer. Thanks again

4. Jul 19, 2015

### SteamKing

Staff Emeritus
Is x2 + y2 = 5 the equation of a cylinder of radius = 5?

https://en.wikipedia.org/wiki/Circle

5. Jul 19, 2015

### Phil Frehz

That's how the book stated the problem, I understood it as the cylinder created when the circle x2 + y2 = 5 is extended between z=0 and z=1

6. Jul 19, 2015

### SteamKing

Staff Emeritus
Since the sections thru the cylinder along the z-axis are circles, then the equation of the circle,
namely x2 + y2 = r2, must be satisfied.

If the radius of the circular sections of the cylinder is indeed r = 5, then what must the equation of the cylinder be?