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Homework Help: Largest possible volume of a cylinder inscribed in a cone

  1. Dec 4, 2008 #1
    1. The problem statement, all variables and given/known data

    A right circular cylinder is inscribed in a cone with height h and base radius r. Find the largest possible volume of such a cylinder.

    I'm just really confused on how to figure this one out. The equation for the volume of a cone is v = 1/3pi r^2h and the volume of a cylinder is v = pi r^2h. I just don't know how to use these two formuals in order to find a solution. Please help me. Thanks.
  2. jcsd
  3. Dec 4, 2008 #2


    User Avatar
    Science Advisor

    Re: Optimization

    Draw a picture. Draw a coordinate system so and two lines, one through (r, 0) and (0, h) and the other through (-r, 0) and (0, h). That represents your cone. What are the equations of the lines? A cylinder inside the cone is represented by a rectangle in your picture. What are the dimensions of that cylinder?
  4. Dec 4, 2008 #3
    Re: Optimization

    The problem didn't state any dimesions or equations for the cylinder or cone.
  5. Dec 5, 2008 #4


    Staff: Mentor

    Re: Optimization

    From your first post:
    r and h are the dimensions of the cone. Follow Halls's suggestion to draw a picture and label the important points.
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