+1982 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
+129852 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
