Finding largest volume of right circular cone inscribed in a sphere of radius 3

Discussion in 'Calculus' started by Eulers_Disciple, Sep 6, 2023.

  1. Eulers_Disciple


    Sep 6, 2023
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    I would like some assistance solving the applied optimization problem in my my calculus book that ask that you find the largest volume for a right circular cone inscribed in a sphere of radius 3. The book provides an image [​IMG]
    I would like some tips on where exactly I must start as I thought I had to solve for x then get y in terms of the radius r and then input that into my volume equation for the right circular cone then take the first derivative and solve for r to get the optimal value of r for the volume.
    Eulers_Disciple, Sep 6, 2023
  2. Eulers_Disciple


    Aug 13, 2023
    Likes Received:
    Start with what you know:

    * the formula for the volume of a sphere
    * the formula for the volume of a cone

    From the picture:

    * the radius of the base of the cone
    * the expression for the height of the cone
    * the radius of the sphere
    * the Pythagorean Theorem

    Use the Pythagorean Theorem to express y in terms of x. See where that leads....
    e.jane.aran, Sep 6, 2023
    Ian and sologuitar like this.
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