September 2022
Problem of the Month

Ten Circles in a "Pyramid"

Ten circles of radius m are stacked together as shown in the diagram below.

Determine the distance from the top of the "pyramid" to the bottom.

Solution:

The height of the pyramid
is   3 √ 3 m + 2 m   ~   3.732 m



△ ABC is equilateral (each side is 6 m)
AD = 3 m
m ∠ A = 60°
m ∠ ADC = 90°
CD = 3 √ 3 m
So height of the pyramid is 3 √ 3 m + 2m

Correctly solved by:

1. Davit Banana	Istanbul, Turkey
2. Colin (Yowie) Bowey	Beechworth, Victoria, Australia
3. Dr. Hari Kishan	D.N. College, Meerut, Uttar Pradesh, India
4. Ritwik Chaudhuri	Santiniketan, West Bengal, India

Send any comments or questions to: David Pleacher