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A coin made of alloy of aluminum and silver measures 2 x 15

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A coin made of alloy of aluminum and silver measures 2 x 15 [#permalink]

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New post 27 Nov 2007, 20:14
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A coin made of alloy of aluminum and silver measures 2 x 15 mm (it is 2 mm thick and its diameter is 15 mm). The weight of the coin is 30 grams and the volume of aluminum in the alloy equals that of silver. What will be the weight of the coin measuring 1 x 30 mm made of pure aluminum if silver is twice heavier than aluminium?

(A) 36 grams
(B) 40 grams
(C) 42 grams
(D) 48 grams
(E) 50 grams

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New post 27 Nov 2007, 20:34
I got B..

Volume of first coin is 56.25(2pi). (volume of cylinder)

So, volume of aluminium portion 56.25 pi.

Because total weight is 30g, AL:AG ratio is 10:20.

Volume of second coin is 225(1pi) its all aluminium


56.25 pi has 10 g
So, 225 pi will have (225*10)/56.25 = 40 g

Whats the OA

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Re: PS: Aluminium and silver [#permalink]

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New post 27 Nov 2007, 21:40
eyunni wrote:
A coin made of alloy of aluminum and silver measures 2 x 15 mm (it is 2 mm thick and its diameter is 15 mm). The weight of the coin is 30 grams and the volume of aluminum in the alloy equals that of silver. What will be the weight of the coin measuring 1 x 30 mm made of pure aluminum if silver is twice heavier than aluminium?

(A) 36 grams
(B) 40 grams
(C) 42 grams
(D) 48 grams
(E) 50 grams


V of cylinder is pir^2h ---> 7.5^2*2=112.5pi

56.25=V of S
56.25=V of A

30grams 2A=S so we have 10grams of A 20 grams of S

Vol of pure A coin. 15^2(1)(pi)=225pi

Do a ratio.

10grams/56.25pi(vol)=x/225pi(vol)

56.25pix=2250(g)pi cancel out the pi's. x=40.

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Re: PS: Aluminium and silver [#permalink]

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New post 27 Nov 2007, 22:08
eyunni wrote:
A coin made of alloy of aluminum and silver measures 2 x 15 mm (it is 2 mm thick and its diameter is 15 mm). The weight of the coin is 30 grams and the volume of aluminum in the alloy equals that of silver. What will be the weight of the coin measuring 1 x 30 mm made of pure aluminum if silver is twice heavier than aluminium?

(A) 36 grams
(B) 40 grams
(C) 42 grams
(D) 48 grams
(E) 50 grams


Get B.

Wt of 1st coin = 30 g
Since silver is twice the wt. of aluminum, wt of silver = 20 g and wt of aluminum = 10g

V = (7.5)^2 * 2*pi
Since volume of aluminum = volume of silver, volume of silver = (7.5)^2 *pi

volume of 2nd coin = (15)^2 * pi
Since (7.5)^2* pi represents 10 g of aluminum, (15)^2 * pi will represent:
(10 * 15^2*pi)/(7.5^2*pi) = 40

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New post 29 Nov 2007, 07:16
sorry for the delay. OA is B.

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New post 19 Dec 2007, 01:18
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A coin is essentially a very flat cylinder.
Volume of a cylinder = Area of circle * Height

Volume of 1st coin
V = pi* (r^2) * H
V = pi * 56.25 * 2
V = 112.5pi

Volume of 2nd coin
V = pi* (r^2) * H
V = pi 225
Thus, the volume of the second coin is twice the first coin.

A + S = 30 grams
A + 2A = 30
A = 10 grams

Since the second coin is all aluminum, we can assume the first coin is all aluminum and that it would weigh 20 grams. Since the second coin is twice the weight of the first coin, the second coin is 40 grams.

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Re: A coin made of alloy of aluminum and silver measures 2 x 15 [#permalink]

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Re: A coin made of alloy of aluminum and silver measures 2 x 15   [#permalink] 02 Oct 2017, 02:08
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