11. Parametric Surfaces and Surface Integrals

Surface Area — Quiz

Test your understanding of surface area with 5 practice questions.

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Practice Questions

Question 1

Which formula gives the surface area of a parametric surface $\mathbf r(u,v)$ over a region $D$ in the parameter plane?

Question 2

For a surface written as a graph $z=f(x,y)$, which expression is the surface area element?

Question 3

What is the area of the surface parameterized by $\mathbf r(u,v)=\langle u,v,0\rangle$ for $0\le u\le 2$ and $0\le v\le 3$?

Question 4

What is the surface area of the part of the plane $z=2x+3y$ lying above the unit square $0\le x\le 1$ and $0\le y\le 1$?

Question 5

What is the surface area of the cylinder parameterized by $\mathbf r(\theta,z)=\langle\cos\theta,\sin\theta,z\rangle$ for $0\le\theta\le 2\pi$ and $0\le z\le 4$?