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

[Brown Arrow]

Homework Statement

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

Homework Equations

N/A

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

 

[LCKurtz]

Your picture shows a cone that is inscribed inside a sphere, not circumscribed outside as the problem asks.

 

[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

 

[I like Serena]

Homework Statement

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

Homework Equations

N/A

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

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.

 

[LCKurtz]

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.