Only Pure Think

Quiz 70: 4 balls height
Which is the height H from the base till the top of 4 balls having diameter D placed as in the sketch?

Well, the solution is quite simple.

a) The three balls on bottom, have the centers in a plane at R=D/2 from the base.
b) These 3 centers, with the center of the forth ball, form a regular pyramid (regular tetrahedron) with sides D long. The height of this pyramid is sqr(2/3)D.
c) From the center of the forth ball, R=D/2 is missing to reach the top.

Therefore the distance is a)+b)+c)=[1+sqr(2/3)]D

Congratulations to Darixsem!

Solution [1+sqr(2/3)]D

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