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

by Brown Arrow
Tags: cone, minimum, sense, volume
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Brown Arrow
#1
Mar22-11, 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
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LCKurtz
#2
Mar22-11, 12:29 AM
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Your picture shows a cone that is inscribed inside a sphere, not circumscribed outside as the problem asks.
Brown Arrow
#3
Mar22-11, 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

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#4
Mar22-11, 04:01 AM
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Find the Minimum Volume of cone, answer does not make sense

Quote Quote by Brown Arrow View Post
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
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
#5
Mar22-11, 11:51 AM
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Quote Quote by Brown Arrow View Post
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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