Lenny Conundrum 221

Jerch · **Posts:** 329 **Joined:** Sun Sep 25, 2005 6:19 am

Quote:

A Two Hundred Dubloon Coin is unique in that the outer edge is gold while the inside is silver. Assuming both sides of the coin are identical, and a line tangent to the inner circle is 23 mm from edge to edge of the coin, and excluding the edge of the coin in the calculation, what is the surface area of gold on the coin, in square millimetres? Please round up to the nearest square millimetre.

Well...back to maths.

Anyway, I believe that they've assumed that the outer and inner 'ring/circle' are concentric.

chibis223 · **Posts:** 1 **Joined:** Fri Jul 06, 2007 4:22 pm

Actually, all you REALLY need to know is:

Duke of Earl · **Posted:** Fri Jul 06, 2007 5:27 pm

chibis223 wrote:

Actually, all you REALLY need to know is:

That's so fundamental though... :p.

It would seem to me that you need to do some pixel measurements to determine a few numbers you need anyway. Or else I missed a key point.

Regan · **Posted:** Sat Jul 07, 2007 4:11 am

This question makes me groan only because it's been a few years since I've been in any math related classes and I could have easily answered this question if I were just a bit younger. Bah.

draconis · **Posted:** Sat Jul 07, 2007 10:34 am

I accidentally multiplied my answer by two, because I forgot I already doubled the values to consider both sides, so my final answer is definitely wrong. Pfft, what a waste of a LC I actually understood.

AySz88 · **Posted:** Thu Jul 19, 2007 11:54 pm

Duke of Earl wrote:

It would seem to me that you need to do some pixel measurements to determine a few numbers you need anyway. Or else I missed a key point.

No need.
Let r = smaller radius, a = difference between smaller and larger radii.

Area = 2*pi*[(r+a)^2-r^2]

Right triangle formed by one large radius, one small radius, and the line:
11.5^2 + r^2 = (r+a)^2
--> r^2 = (r+a)^2 - 11.5^2

Plug into area formula:

Area = 2*pi*[(r+a)^2-((r+a)^2 - 11.5^2)] = 2*pi*[~~(r+a)^2 - (r+a)^2~~ + 11.5^2)]
= 2*pi*11.5^2
= 830.951 ~= 831

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