Lenny Conundrum Round 221: area of gold on coin

[dorian]

First, look at this picture...



And then this:

I need help to solve this problem... I have NO clue as to what the answer is :shock: , but the picture is part of a riddle, and the riddle is as follows:

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.

PLEASE help me with this extremely hard question!!

thanks
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Edited by stapel -- Reason for edit: clarification

 

[stapel]

I need help to solve this problem...PLEASE help me with this extremely hard question!!

Actually, this isn't a particularly difficult "Lenny Conundrum" weekly-contest question. Many Neopians were turning in their answer within minutes of the new puzzler being posted.

Note: Many (most?) tutoring services would have immediately deleted your post and banned you from the site for having abused this tutoring service by pretending this contest question is homework. But, according to some Neopians, some educators actually assign these contest questions to their underage students in hopes that the children will win prizes for them. (How pathetic!)

Because it is possible that this abuse was not generated by you, your account will not be closed at this time. However, since Neopets has been quite clear regarding its position on the prize-winning answers being posted at places like this before the contest closes, we will respect Neopets' policy and not post the solution until after the evening of 11 July 2007, at the earliest.

If you would like to attempt the puzzler, please reply showing your work and reasoning so far, and we'll be glad to provide hints and suggestions to help you figure this out for yourself. On the other hand, if this was assigned to you (so the reason you're lost is that you haven't learned this material yet), then you might want to print out this thread and show it to your parents, so that responsible adults can take appropriate corrective action.

Eliz.

 

[TchrWill]

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.

Let r1 = the radius of the inner circle from the center perpendicular to the given chord.
Let r2 = the radius of the outer circle from the center to the end of the chord.
Half the chord, C, = 11.5mm.
Therefore, r1^2 + 11.5)^2 = r2^2
r2^2 - r1^2 = 132.25 = 26.45x5
(r2 + r1)(r2 - r1) = 26.45x5
(r2 + r1) = 26.45
(r2 - r1) = 5
Adding, 2r2 = 31.45 or r2 = 15.725mm and r1 = 10.725mm
A2 = 3.14(15.725)^2 = 776.84 sq.mm
A1 = 3.14(10.725)^2 = 361.36 sq.mm
Agold = A2 - A1 = 415.47 sq.mm per side
Asilver = 363.06 sq.mm per side.

Actually, the gold area derives directly from Ag = Pir2^2 - Pir2^2 = Pi(r2^2 - r1^2 = Pi(C/2)^2 = 415.47 sq.mm per side.