Question

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 hı to the height of a parallelogram pack h2?
Need it quickly please

Answer 1

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

Explanation:

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