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A soda company wants to efficiently pack 9 cans of soda in one box. Each soda can has a radius r.

What is the ratio of the height of a rectangular pack h1 to the height of a parallelogram pack h2?

A. 2 : 1 + √3

B. 6 : 2 + √3

C. 3 : 1 + √3

D. 6 : 1 + 2√3

 Apr 4, 2019
 #1
avatar+99237 
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The height of the rectangular pack  =  6r   =   h1

 

The  height of the parallelogram  =  2r  + the height of two equilateral triangles with a side of 2r

 

The height of  one equilateral triangle  with a side of 2r  = (side)/ 2 * √3  = (2r) / 2 * √3  =   r√3

 

So....the height of two of these is   2r√3

 

So... the height of the parallelogram =  2r  +  2r√3   =   2  ( 1 + √3   )   =   h2

 

So.....the ratio  of    h1   to h2   =  

 

6 :  2 ( 1 + √3)   =        {  divide by  2 }

 

3 :   1 + √3

 

 

cool cool  cool

 Apr 4, 2019

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