Paul's Online Notes
Home / Calculus III / Surface Integrals / Parametric Surfaces
Show Mobile Notice Show All Notes Hide All Notes
Mobile Notice
You appear to be on a device with a "narrow" screen width (i.e. you are probably on a mobile phone). Due to the nature of the mathematics on this site it is best views in landscape mode. If your device is not in landscape mode many of the equations will run off the side of your device (should be able to scroll to see them) and some of the menu items will be cut off due to the narrow screen width.

### Section 6-2 : Parametric Surfaces

For problems 1 – 6 write down a set of parametric equations for the given surface.

1. The plane $$7x + 3y + 4z = 15$$. Solution
2. The portion of the plane $$7x + 3y + 4z = 15$$ that lies in the 1st octant. Solution
3. The cylinder $${x^2} + {y^2} = 5$$ for $$- 1 \le z \le 6$$. Solution
4. The portion of $$y = 4 - {x^2} - {z^2}$$ that is in front of $$y = - 6$$. Solution
5. The portion of the sphere of radius 6 with $$x \ge 0$$. Solution
6. The tangent plane to the surface given by the following parametric equation at the point $$\left( {8,14,2} \right)$$. $\vec r\left( {u,v} \right) = \left( {{u^2} + 2u} \right)\vec i + \left( {3v - 2u} \right)\vec j + \left( {6v - 10} \right)\vec k$ Solution
7. Determine the surface area of the portion of $$2x + 3y + 6z = 9$$ that is inside the cylinder $${x^2} + {y^2} = 7$$. Solution
8. Determine the surface area of the portion of $${x^2} + {y^2} + {z^2} = 25$$ with $$z \le 0$$. Solution
9. Determine the surface area of the portion of $$z = 3 + 2y + \frac{1}{4}{x^4}$$ that is above the region in the $$xy$$-plane bounded by $$y = {x^5}$$, $$x = 1$$ and the $$y$$-axis. Solution
10. Determine the surface area of the portion of the surface given by the following parametric equation that lies inside the cylinder $${u^2} + {v^2} = 4$$. $\vec r\left( {u,v} \right) = \left\langle {2u,vu,1 - 2v} \right\rangle$ Solution