Find the Minimum Volume of cone, answer does not make sense

  1. 1. The problem statement, all variables and given/known data

    Find the Dimensions of the right circular cone of minimum volume which can be circumscribed about a sphere of radius 8 inches.

    2. Relevant equations


    3. The attempt at a solution
    So this is my try, i did the question to find the minimum volume of the cone,
    For Larger Size:
    As you can see the minimum value is when h=0 , thus volume is equal to 0, it makes sense the minimum volume would be 0, but i think i did the question wrong, can you tell me where i've gone wrong.

    Please help
  2. jcsd
  3. LCKurtz

    LCKurtz 8,448
    Homework Helper
    Gold Member

    Your picture shows a cone that is inscribed inside a sphere, not circumscribed outside as the problem asks.
  4. so is it suppose to be like this then i try to minimize the volume of the cone,
    sorry i didn't get what it meant mean circumscribed , i though it would be inside
  5. I like Serena

    I like Serena 6,183
    Homework Helper

    Your calculation (given your drawing) is completely correct.
    It's only your graphic interpretation with a parabola that is incorrect.
    The volume is not given by a parabola but by a third power.
    So the maximum volume is at h=32/3.
    Btw, the volume becomes zero at h = 16, which is the solution for V=0.
  6. LCKurtz

    LCKurtz 8,448
    Homework Helper
    Gold Member

    Yes. But your picture needs a little work. The bottom of the sphere would touch the center of the base of the cone.
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