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Homework Help: 3d Shapes (Multivar. Calc)

  1. Sep 10, 2011 #1
    1. The problem statement, all variables and given/known data
    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.

    2. Relevant 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]?

    3. 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.
  2. jcsd
  3. Sep 10, 2011 #2


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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: Sep 10, 2011
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