Parametric Equation of Surface

[Phil Frehz]

Homework Statement

Find parametric equations for the portion of the cylinder x² + y² = 5 that extends between the planes z = 0 and z=1.

Homework Equations

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

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

 

[Mark44]

Homework Statement

Find parametric equations for the portion of the cylinder x² + y² = 5 that extends between the planes z = 0 and z=1.

Homework Equations

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

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

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.

 

[Phil Frehz]

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.

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

 

[SteamKing]

Homework Statement

Find parametric equations for the portion of the cylinder x² + y² = 5 that extends between the planes z = 0 and z=1.

Homework Equations

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

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

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

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

 

[Phil Frehz]

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

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

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

 

[SteamKing]

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

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?