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A circular sheet of paper of radius 6 inches is cut into 3 equal sectors, and each sector is formed into a cone with no overlap. What is the height in inches of the cone?

Guest Jun 25, 2018
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The  circumference of  the base  of each cone will be the arc length of one of the sectors  =

 

2 pi (6)  / 3  =  4 pi  inches

 

So....the radius, r, of each cone (in inches) is given  by :

 

4pi  =  2 pi * r

4  = 2r

2  = r   

 

And the slant height of each cone  is the radius of the original circle

 

And the radius of the cone and its height will form two legs of a right triangle with a hypotenuse of 6 inches  (the slant height)

 

So...using the Pythagorean Theorem, the cone height, h, is given by :

 

h  = √[ slant height^2  - radius^2 ]  =  √ [ 6^2  - 2^2 ] = √32  =  4√2  inches

 

 

cool cool cool

CPhill  Jun 25, 2018

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