Let's Play With Rings!

Geometry Level pending

A certain type of ring has an outer diameter of 58 mm and an inner diameter of 40 mm and a thickness of 1 mm. If one stacks enough rings on top of each other, it is possible to stand another ring vertically on top of the pile in such a way that the ring doesn’t touch the ground. What is the minimum number of rings you need to stack on top of each other so that the vertical ring just doesn’t touch the ground?

This was problem 9 on the South African Mathematics Olympiad (Junior Round 3 Paper 2012)


The answer is 8.

Mark Mottian by Mark Mottian , 22, South Africa

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1 solution

Alex Zhong
Apr 10, 2015

The vertical ring and the top horizontal ring form a right triangle with the hypotenuse as 29 and the horizontal leg as 20. We have the vertical leg as 2 9 2 − 2 0 2 = 21. \sqrt{29^2-20^2}=21. Therefore, we need 29 − 21 = 8 29-21=\boxed{8} rings stacks up, (1mm thick) to support the vertical ring.

1 Helpful 0 Interesting 0 Brilliant 0 Confused

can u explain further?? how hypotenuse of 29 etc

Nithin Nithu - 6 years, 2 months ago

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Radii of rings: 58/2 = 29, 40/2 =20

Alex Zhong - 6 years, 2 months ago

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