What is the Height of a Cone Confined to a Hemisphere with Given Radius?

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In summary: It cannot. In summary, the problem is to find the height of a cone with a base that matches the base of a hemisphere with a radius of r. Pythagoras' theorem can be used to find the relationship between the height and radius of the cone. The resulting function can then be used to find the minimum height of the cone.
  • #1
leprofece
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(1) Confine to a hemisphere of RADIUS r a volume minimum Cone; the plane of the base of the cone matches with the basis of the hemisphere. Find the height of the cone.

Answer is H = (sqrt of 3) R
 
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  • #2
I think if the two objects have their bases in the same plane, the the height of the cone must be the same as the radius of the hemisphere, so I think more likely the case is that the vertex of the cone on on the base of the hemisphere. Even so I get a result that is very similar to, but critically different than what you have given.

1.) What is your objective function?

2.) Can you express the radius of the cone in terms of the radius of the hemisphere and the height of the cone? Look at a cross-section through the center of both objects and Pythagoras will be your friend.

What do you find?
 
  • #3
Ok it is a problem of derivative applications Maximum and minimum we must get two functions and derive one to get the minimum.
In this problem I don't have idea of the functions maybe the volume of the cone and thales
as i said before they are very difficult problems.
 
  • #4
leprofece said:
Ok it is a problem of derivative applications Maximum and minimum we must get two functions and derive one to get the minimum.
In this problem I don't have idea of the functions maybe the volume of the cone and thales
as i said before they are very difficult problems.

I edited your post to remove your email address. It is not a good idea to publicly post your email addy and it is not our policy to email solutions anyway. It is best to respond in the threads.

Did you try what I suggested? It really makes the problem fall into place. :D

Do you see how the result you posted is impossible? How can the height of the cone be greater than the radius of the hemisphere?
 

FAQ: What is the Height of a Cone Confined to a Hemisphere with Given Radius?

What is the definition of max and min?

Max and min refer to the maximum and minimum values of a set of data or a function. The maximum value is the largest value in the set, while the minimum value is the smallest value.

How do you find the max and min of a set of numbers?

To find the max and min of a set of numbers, you can arrange the numbers in ascending or descending order and then the first and last numbers will be the min and max, respectively. Alternatively, you can use a calculator or computer program to find the max and min values.

Can a set of numbers have more than one max or min value?

Yes, a set of numbers can have more than one max or min value if there are multiple numbers that are tied for the largest or smallest value. For example, in the set {1, 2, 3, 3, 3, 4}, the max value is 4 and the min value is 1, but there are multiple numbers with the same value of 3.

How are max and min used in real-life applications?

Max and min are commonly used in various fields such as economics, statistics, and engineering. In economics, they can be used to determine the maximum profit or minimum cost of a business. In statistics, they are used to analyze data and identify outliers. In engineering, they are used to optimize designs and determine the maximum or minimum values of certain parameters.

What is the difference between local max/min and global max/min?

A local max or min refers to the largest or smallest value within a specific interval or region, while a global max or min refers to the largest or smallest value over the entire domain. In other words, a local max/min is a relative extremum, while a global max/min is an absolute extremum. This concept is often used in calculus and optimization problems.

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