15.5 Parametric Surfaces 935
15.5 Parametric Surfaces
Multiple Choice
Identify the choice that best completes the statement or answers the question.
____ 1. Match the following vector-valued function with its graph.
a. d.
b. e.
936 Chapter 15: Vector Analysis
c.
____ 2. Match the following vector-valued function with its graph.
a. d.
15.5 Parametric Surfaces 937
b. e.
c.
____ 3. Find the rectangular equation for the surface by eliminating parameters from the
vector-valued function. Identify the surface.
a.
b.
c.
d.
e.
938 Chapter 15: Vector Analysis
____ 4. Find the rectangular equation for the surface by eliminating the parameters from the
vector-valued function .
a.
b.
c.
d.
e.
____ 5. Identify the surface by eliminating the parameters from the vector-valued function
.
a. plane
b. sphere
c. paraboloid
d. cylinder
e. ellipsoid
____ 6. Find the rectangular equation for the surface by eliminating the parameters from the
vector-valued function and sketch the graph.
a. d.
15.5 Parametric Surfaces 939
b. e.
c.
____ 7. Find a vector-valued function whose graph is the plane .
a.
b.
c.
d.
e.
940 Chapter 15: Vector Analysis
____ 8. Find a vector-valued function whose graph is the cone .
a.
b.
c.
d.
e.
____ 9. Find a vector-valued function whose graph is the cylinder .
a.
b.
c.
d.
e.
____ 10. Find a vector-valued function whose graph is the ellipsoid .
a.
b.
c.
15.5 Parametric Surfaces 941
d.
e.
____ 11. Find a vector-valued function whose graph is the ellipsoid .
a.
b.
c.
d.
e.
____ 12. Find a vector-valued function whose graph is the part of the paraboloid
that lies inside the cylinder .
a.
b.
c.
d.
e.
942 Chapter 15: Vector Analysis
a.
b.
c.
d.
e.
____ 14. Write a set of parametric equations for the surface of revolution obtained by
revolving the graph of the function about the x-axis.
a.
b.
c.
d.
e.
____ 13. Write a set of parametric equations for the surface of revolution obtained by
revolving the graph of the function about the given axis.
15.5 Parametric Surfaces 943
____ 15. Find an equation of the tangent plane to the surface represented by the vector-valued
function at the given point.
a.
b.
c.
d.
e.
____ 16. Find the area of the surface given by , where
.
a.
b.
c.
d.
e.
____ 17. Find the area of the surface over the given region. Use a computer algebra system to
verify your results.
The sphere,
a.
b.
c.
d.
e.
944 Chapter 15: Vector Analysis
a.
b.
c.
d.
e.
____ 19. Find the area of the surface of revolution
.
a.
b.
c.
d.
e.
____ 20. The surface of the dome on a new museum is given by
and is in
meters. Find the surface area of the dome.
a.
b.
c.
d.
e.
____ 18. Find the area of the surface over the given region. Use a computer algebra system to
verify your results.
The part of the cone,
where .
15.5 Parametric Surfaces 945
____ 21. Find a vector-valued function for the hyperboloid .
a.
b.
c.
d.
e.
____ 22. Determine the tangent plane for the hyperboloid .
a.
b.
c.
d.
e.
946 Chapter 15: Vector Analysis
15.5 Parametric Surfaces – Answer Section