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Master | Next Rank: 500 Posts
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by nafiul9090 » Sun Sep 11, 2011 8:18 am
A cylindrical tank has a base with a circumference of 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?
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by sl750 » Sun Sep 11, 2011 9:02 am
In terms of the radius, the length of one side of the equilateral triangle is sqrt(3)*r
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by cans » Sun Sep 11, 2011 9:25 am
cylindrical base: circle.
area of base = pi* r^2.
area of triangle = root(3)/4 * a^2.
p(inside base)=1 - 3/4 = 1/4 = [root(3)/4 * a^2] /[pi* r^2]
a^2 = pi * r^2 / root(3)
Thus we can get a.
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