Question
Find the area of the surface.The part of the paraboloid $ y = x^2 + z^2 $ that lies within the cylinder $ x^2 + y^2 = 16 $
Step 1
The equation of the paraboloid $y = x^2 + z^2$ can be written as $y = r^2$ where $r = \sqrt{x^2 + z^2}$. The equation of the cylinder $x^2 + y^2 = 16$ can be written as $r^2 = 16$ or $r = 4$. Show more…
Show all steps
Your feedback will help us improve your experience
Frank Lin and 87 other Calculus 3 educators are ready to help you.
Ask a new question
Labs
Want to see this concept in action?
Explore this concept interactively to see how it behaves as you change inputs.
Key Concepts
Recommended Videos
Find the surface area of the given surface. The portion of the paraboloid $z=x^{2}+y^{2}$ inside the cylinder $x^{2}+y^{2}=4$
Vector Calculus
Surface Integrals
Find the area of the given surface. The portion of the paraboloid $2 z=x^{2}+y^{2}$ that is inside the cylinder $x^{2}+y^{2}=8$
Multiple Integrals
Parametric Surfaces; Surface Area
Find the area of the surface. $$\begin{array}{l}{\text { The part of the paraboloid } x=y^{2}+z^{2} \text { that lies inside the }} \\ {\text { cylinder } y^{2}+z^{2}=9}\end{array}$$
Parametric Surfaces and Their Areas
Transcript
18,000,000+
Students on Numerade
Trusted by students at 8,000+ universities
Watch the video solution with this free unlock.
EMAIL
PASSWORD