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

by Brown Arrow
Tags: cone, minimum, sense, volume
 P: 101 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 N/A 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: http://i54.tinypic.com/29yqyiw.jpg 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
 HW Helper Thanks PF Gold P: 7,655 Your picture shows a cone that is inscribed inside a sphere, not circumscribed outside as the problem asks.
 P: 101 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
HW Helper
P: 6,187
Find the Minimum Volume of cone, answer does not make sense

 Quote by Brown Arrow 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 N/A 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: http://i54.tinypic.com/29yqyiw.jpg 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
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.
HW Helper
Thanks
PF Gold
P: 7,655
 Quote by Brown Arrow 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
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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