Practice: Surfaces & Area

8 multiple choice · 4 free response · 1 walkthroughs

Q1.

basic

Surface area of

z = f (x, y)

over region

R

equals

Q2.

intermediateSurface Integrals T/F #2

True/False:

∣ r_{u} \times r_{v} ∣

depends on the orientation of the surface.

Q3.

intermediateSurface Integrals T/F #4

True/False: A surface is **orientable** if a continuous unit normal vector field can be defined on it.

Q4.

basicSurface Integrals T/F #8

True/False: Surface area depends on which orientation you choose.

Q5.

basic

Parameterize the cylinder

x^{2} + y^{2} = 4, 0 \leq z \leq 5

via

Q6.

intermediate

For the parametric surface

r (u, v) = ⟨ u, v, u + v ⟩

(u, v) \in [0, 1]^{2}

, the area is

Q7.

basic

Number of parameters needed to parameterize a 2D surface in

R^{3}

Q8.

basicSurface Integrals T/F #3

True/False: A surface can have multiple orientations, but only one is chosen at a time.