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Find the Minimum Volume of cone, answer does not make sense 
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#1
Mar2211, 12:27 AM

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 


#2
Mar2211, 12:29 AM

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.



#3
Mar2211, 12:35 AM

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 


#4
Mar2211, 04:01 AM

HW Helper
P: 6,187

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


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