Surface Integrals Quizzes, Questions & Answers

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3D Geometry: Identifying Quadric Surfaces Quiz

This educational tool focuses on matching equations to their corresponding quadric surfaces, enhancing comprehension in mathematical 3D geometry. It's designed to test and reinforce knowledge, crucial for students in advanced...

Questions: 6 | Attempts: 14 | Last updated: Aug 11, 2025

Sample Question 1
What is the equation of an ellipsoid in 3D space?

X^2/a^2 - y^2/b^2 + z^2/c^2 = 1

X^2/a + y^2/b + z^2/c = 1

X^2/a^2 + y^2/b^2 + z^2/c^2 = 1All Traces are ellipsesIf a=b=c, sphere

X/a + y/b + z/c = 1

Sample Question 2
Cone

Z^2/c^2 = x^2/a^2 + y^2/b^2Horizontal Traces are ellipsesVertical traces in planes x=k and y=k are hyperbolas if k is not 0, a pair of lines if k=0

Z^2/c = x/a + y/b. This equation results in a plane when graphed.

Z^2/c^2 = x^2/a^2 - y^2/b^2. The traces result in parabolas in this case.

Z/c = x^2/a - y^2/b. The traces will form circles in this scenario.

Sample Question 3
What is the equation for an Elliptic Paraboloid?

Z/c= x^2/a^2 + y^2/b^2Horizontal Traces are ellipsesvertical traces are parabolasVariable raised to the first power indicates axis of paraboloid

Z = x^2 - y^2

Z = x^2/a^2 - y^2/b^2

Z = x^2 + y^2