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!

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

Awards:

Awards:

Position | Name | Points | Time | Country | User |
---|---|---|---|---|---|

1 | Darixsem | 20 | 6.17:59:54 | Italy | Free |