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manhattan 700+ quistion

by ankurmit » Thu Jul 08, 2010 10:19 pm
Please solve this:

A cylindrical tank has a base with a area of 4.(3)^(1/2) meters and an equilateral triangle painted on the interior side of the base. A grain of sand is dropped into the tank, and has an equal probability of landing on any particular point on the base. If the probability of the grain of sand landing on the portion of the base outside the triangle is 3/4, what is the length of a side of the triangle?


a. 4
b. 2
c. 3^1/2
d. 1/2
e. 2/3
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by Rahul@gurome » Thu Jul 08, 2010 10:46 pm
Area of base is a circle = 4√3
Probability of the grain of sand landing on the portion of the base outside the triangle is 3/4, so probability of the grain of sand landing on the portion of the base inside the triangle is 1/4.
So, area of equilateral triangle = (1/4)(Area of circle) = √3

If a is the side of equilateral triangle, area of equilateral triangle = (1/2)(base)(height) = (1/2)(a)(a√3/2) = (a^2)(√3/4)
We earlier found that area of equilateral triangle = √3, so (a^2)(√3/4) = √3, which implies a^2 = 4 or a=2

The correct answer is (B).
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by ankurmit » Thu Jul 08, 2010 11:30 pm
thanks Rahul..nice explanation..I am not able to draw its figure. Can you please help me
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by Rahul@gurome » Thu Jul 08, 2010 11:45 pm
ankurmit wrote:thanks Rahul..nice explanation..I am not able to draw its figure. Can you please help me
Here's the figure, it shows the base of cylindrical tank. Hope this helps.

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by ankurmit » Thu Jul 08, 2010 11:47 pm
Nice figure :)

Thanks again
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by Rahul@gurome » Thu Jul 08, 2010 11:53 pm
ankurmit wrote:Nice figure :)

Thanks again
welcome :-)
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