Hi bhushan288, and welcome to Gmat Club.

Please read and follow: how-to-improve-the-forum-search-function-for-others-99451.html

So please:
Provide answer choices for PS questions.
Make sure you type the question in exactly as it was stated from the source.

Also:
Please post PS questions in the PS subforum: gmat-problem-solving-ps-140/
Please post DS questions in the DS subforum: gmat-data-sufficiency-ds-141/

No posting of PS/DS questions is allowed in the main Math forum.

Original question is:

A cylindrical tank has a base with a circumference of 4(sqrt(pi sqrt(3)) 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. \sqrt{2{\sqrt{6}}

B. \frac{\sqrt{6{\sqrt{6}}}}{2}

C. \sqrt{2{\sqrt{3}}

D. \sqrt{3}

E. 2

Given: circumference=4\sqrt{\pi{\sqrt{3}} and P(out)=\frac{3}{4}

Now, as the probability of the grain of sand landing on the portion of the base outside the triangle is 3/4 then the the portion of the base (circle) outside the triangle must be 3/4 of the are of the base and the triangle itself 1/4 of the are of the base.

Next: circumference=4\sqrt{\pi{\sqrt{3}}}=2\pi{r} --> square both sides --> 16\pi{\sqrt{3}}=4{\pi}^2{r}^2 --> 4{\sqrt{3}}={\pi}{r}^2 --> area_{base}=\pi{r^2}=4{\sqrt{3}};

The area of the equilateral triangle is 1/4 of the base: area_{equilateral}=\frac{1}{4}*4{\sqrt{3}}=\sqrt{3} --> also the ares of the equilateral triangle is area_{equilateral}=a^2*\frac{\sqrt{3}}{4}, where a is the length of a side --> area_{equilateral}=a^2*\frac{\sqrt{3}}{4}=\sqrt{3} --> a=2.

Answer: E.
_________________

PLEASE READ AND FOLLOW: 11 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory

COLLECTION OF QUESTIONS:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. NEW!!!

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS ; 9 Devil's Dozen!!!; 10 Number Properties set. NEW!!!


What are GMAT Club Tests?
25 extra-hard Quant Tests

Find out what's new at GMAT Club - latest features and updates

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?

a. \sqrt{2[square_root]6}[/square_root]
b. \sqrt{6[square_root]6}[/square_root]/2
c. \sqrt{2[square_root]3}[/square_root]
d. \sqrt{3}
e. 2

real tough one.
_________________

Verbal:new-to-the-verbal-forum-please-read-this-first-77546.html
Math: new-to-the-math-forum-please-read-this-first-77764.html
Gmat: everything-you-need-to-prepare-for-the-gmat-revised-77983.html
-------------------------------------------------------------------------------------------------
Ajit

A cylindrical tank has a base with a circumference of 4(sqrt(pi sqrt(3)) 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. \sqrt{2{\sqrt{6}}

B. \frac{\sqrt{6{\sqrt{6}}}}{2}

C. \sqrt{2{\sqrt{3}}

D. \sqrt{3}

E. 2

Given: circumference=4\sqrt{\pi{\sqrt{3}} and P(out)=\frac{3}{4}

Now, as the probability of the grain of sand landing on the portion of the base outside the triangle is 3/4 then the the portion of the base (circle) outside the triangle must be 3/4 of the are of the base and the triangle itself 1/4 of the are of the base.

Next: circumference=4\sqrt{\pi{\sqrt{3}}}=2\pi{r} --> square both sides --> 16\pi{\sqrt{3}}=4{\pi}^2{r}^2 --> 4{\sqrt{3}}={\pi}{r}^2 --> area_{base}=\pi{r^2}=4{\sqrt{3}};

The area of the equilateral triangle is 1/4 of the base: area_{equilateral}=\frac{1}{4}*4{\sqrt{3}}=\sqrt{3} --> also the ares of the equilateral triangle is area_{equilateral}=a^2*\frac{\sqrt{3}}{4}, where a is the length of a side --> area_{equilateral}=a^2*\frac{\sqrt{3}}{4}=\sqrt{3} --> a=2.

Answer: E.[/quote]

Hello Bunuel

ur explanation is perfect . i just cant understand one thing. i know that formula for the side of equilateral triangle inscribed in the circle
should be a= √3 * r where r is radius and a is side of the triangle, but when using this formula i am not getting the right answer in the above exmpl. what could be the problem? is somth. wrong with formula ? thanks

Ahaaa, got it , thanks
+kudo

could u please explain me why we cant use this formula here ?

The radius of the circumscribed circle is R=a*\sqrt{3}/3

math-triangles-87197.html
_________________

Happy are those who dream dreams and are ready to pay the price to make them come true