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# A cylindrical tank has a base with a circumference of meters and an i

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Manager
Status: Started with mock tests,Kaplan and manhattan score's below
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A cylindrical tank has a base with a circumference of meters and an i  [#permalink]

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01 Dec 2018, 20:49
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Difficulty:

55% (hard)

Question Stats:

53% (01:52) correct 47% (01:46) wrong based on 19 sessions

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A cylindrical tank has a base with a circumference of $$4\sqrt{3π}$$ meters and an isosceles right 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, which of the following is the length of at least one side of the triangle?

A.3
B.12
C.$$\sqrt{2}$$
D.$$\sqrt{3}$$
E.$$\sqrt{6}$$

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A cylindrical tank has a base with a circumference of meters and an i  [#permalink]

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01 Dec 2018, 22:48
$$2\pi r = 4\sqrt{3\pi}$$
square both sides ,
2(πr)^2 = 12π
πr^2 = 6

Let the area of isosceles right triangle be a.
$$\frac{a}{πr^2} = \frac{1}{4}$$
a = 6/4 = 3/2

Let the equal sides be x. Third side = $$x\sqrt{2}$$
Area of triangle = 1/2 * x * x = 3/2
$$x = \sqrt{3}$$
$$x\sqrt{2} = \sqrt{6}$$

E
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Re: A cylindrical tank has a base with a circumference of meters and an i  [#permalink]

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02 Dec 2018, 02:02
A cylindrical tank has a base with a circumference of $$4\sqrt{3π}$$ meters and an isosceles right 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, which of the following is the length of at least one side of the triangle?

A.3
B.12
C.$$\sqrt{2}$$
D.$$\sqrt{3}$$
E.$$\sqrt{6}$$

given :
2*pi*r= 4\sqrt{3pi}

r= 2\sqrt{3*pi}/pi

since its an isosceles triangle so side x:x:x\sqrt{2}

x\sqrt{2}: 2\sqrt{3*pi}/pi
x=\sqrt{6}/\sqrt{pi}

IMO option E is close option..

I m not able to figure out on how to use the given information on Probability of falling grain
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Re: A cylindrical tank has a base with a circumference of meters and an i &nbs [#permalink] 02 Dec 2018, 02:02
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# A cylindrical tank has a base with a circumference of meters and an i

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