3d Shapes (Multivar. Calc)

  • #1

Homework Statement


Give a formula for a function whose graph is described. Sketch it using a computer or a calculator.

A cone of circular cross-section opening downward and with its vertex at the origin.


Homework Equations


I know how to draw the cone and the properties of a cone, so that's not the issue here.

I know the formula of a cone is [tex]x^2 + y^2 = z^2[/tex] but the problem asks for the cone opening downward with the vertex at the origin (so the domain of z would be [0,-inf)). So would the formula simply be [tex]-(x^2 + y^2) = -z^2[/tex]? Furthermore, since they want circular cross-sections, would I insert a constant (i.e. "a") in the formula such that it's something like [tex]-(a^2 +y^2) = -z^2[/tex]?


The Attempt at a Solution


I'm thinking that the formula is [tex]-(x^2 + y^2) = -z^2[/tex] since they want the cone opening downward with the vertex at the origin.
 

Answers and Replies

  • #2
LCKurtz
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x2+y2=z2 gives the full cone opening both upwards and downwards. Multiplying both sides by -1 doesn't change that. What you need to do is solve for z and only take negative values.

[Edit] I didn't notice your cross section question. The cross sections are obtained by setting z = constant.
 
Last edited:

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