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A sphere is composed of multiple cones with the same radius. 

True or False?

Guest May 12, 2018
 #1
avatar+963 
+2

I think this is false. Here is my reasoning:

 

When you look at the 2D version of the sphere, a circle,

 

it is obvious that you can split the circle into equal slices if you cut through the center. 

 

You split the circle into infinitesimally small triangles that is used to contruct a rhombus, hence the proof of the circle's area. 

 

You cannot do the same which a sphere. Split the sphere into infinitesimally small cones from the center, to construct the sphere. But the curved sides of the cone cannot be fitted together, it must be infinitesimally small pyrimaids. 

 

Therefore, a sphere cannot be split into cones, but only pyramids. 

 

I hope this helped,

 

Gavin

GYanggg  May 12, 2018
 #2
avatar+93866 
0

Gavin I think I follow what you are saying and it sounds logical but a cone IS a pyramid.

It is a circular pyramid. So when you say a pyramid I think you are refering to a square or a triangular pyramid..?

Melody  May 13, 2018
 #3
avatar+963 
+1

Hi Melody!
 

In that case, then this is possible. 

 

Using the same logic, a sphere is composed of mulitple cones. 

 

This is because a cone is considered a pyrimaid. 

 

Thank you for correcting my mistake,

 

Gavin

GYanggg  May 13, 2018

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