1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook