Find all School-related info fast with the new School-Specific MBA Forum

 It is currently 19 Jun 2013, 23:55

# A cylindrical tank has a base with a circumference of

Author Message
TAGS:
Intern
Joined: 21 Jun 2010
Posts: 5
Followers: 0

Kudos [?]: 1 [1] , given: 1

A cylindrical tank has a base with a circumference of [#permalink]  28 Nov 2010, 02:04
1
KUDOS
00:00

Question Stats:

60% (04:13) correct 39% (01:02) wrong based on 41 sessions
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
[Reveal] Spoiler: OA

Last edited by Bunuel on 09 Jun 2013, 08:33, edited 2 times in total.
Edited the question and added the OA
GMAT Club team member
Joined: 02 Sep 2009
Posts: 12116
Followers: 1879

Kudos [?]: 10135 [0], given: 965

Re: Probability Triangle(700 lvl Qn ) [#permalink]  28 Nov 2010, 02:43
bhushan288 wrote:
hi guys...
can u help me out with this 1....

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?

Hi bhushan288, and welcome to Gmat Club.

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.

_________________
Intern
Joined: 21 Jun 2010
Posts: 5
Followers: 0

Kudos [?]: 1 [0], given: 1

Re: Probability Triangle(700 lvl Qn ) [#permalink]  28 Nov 2010, 02:51
Thnks a lot Bunuel...
Manager
Joined: 18 Aug 2010
Posts: 91
Followers: 1

Kudos [?]: 3 [0], given: 22

Re: Probability Triangle(700 lvl Qn ) [#permalink]  16 Mar 2011, 07:13
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.

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
Math Forum Moderator
Joined: 20 Dec 2010
Posts: 2098
Followers: 109

Kudos [?]: 667 [1] , given: 376

Re: Probability Triangle(700 lvl Qn ) [#permalink]  16 Mar 2011, 07:32
1
KUDOS
tinki wrote:

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[/quote]

The triangle is not necessarily inscribed because it is not mentioned in the question. It can be any equilateral triangle drawn within the base. The vertices of the triangle may not touch the circle.
_________________
SVP
Joined: 16 Nov 2010
Posts: 1719
Location: United States (IN)
Concentration: Strategy, Technology
Followers: 26

Kudos [?]: 230 [0], given: 35

Re: Probability Triangle(700 lvl Qn ) [#permalink]  17 Mar 2011, 01:40
2*pi*r = 4(sqrt(pi sqrt(3))

=> r = 4(sqrt(pi sqrt(3))/2*pi = 2(sqrt(pi sqrt(3))/pi

Area of circle C = pi * r^2 = 4 * pi* 1/(pi)^2 * pi * sqrt(3) = 4*sqrt(3)

A/C = 1/4

=> A = sqrt(3)

Area of Triangle = sqrt(3) = sqrt(3)/4 * (side)^2

So side = sqrt(4) = 2

_________________

Formula of Life -> Achievement/Potential = k * Happiness (where k is a constant)

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

Senior Manager
Joined: 23 Oct 2010
Posts: 338
Location: Azerbaijan
Followers: 6

Kudos [?]: 69 [0], given: 67

Re: A cylindrical tank has a base with a circumference of [#permalink]  15 Apr 2013, 09:59
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

GMAT Club team member
Joined: 02 Sep 2009
Posts: 12116
Followers: 1879

Kudos [?]: 10135 [1] , given: 965

Re: A cylindrical tank has a base with a circumference of [#permalink]  16 Apr 2013, 03:27
1
KUDOS
LalaB wrote:
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

Because we are told that equilateral triangle is painted so not necessarily inscribed on the interior side of the base.
_________________
Manager
Joined: 09 May 2013
Posts: 53
Followers: 0

Kudos [?]: 6 [0], given: 8

Re: A cylindrical tank has a base with a circumference of [#permalink]  09 Jun 2013, 08:10
Hi Bunuel,
can you explain
how can you consider P(out) as fraction of total base?

Posted from my mobile device
GMAT Club team member
Joined: 02 Sep 2009
Posts: 12116
Followers: 1879

Kudos [?]: 10135 [0], given: 965

Re: A cylindrical tank has a base with a circumference of [#permalink]  09 Jun 2013, 08:39
WarriorGmat wrote:
Hi Bunuel,
can you explain
how can you consider P(out) as fraction of total base?

Posted from my mobile device

Bigger the area bigger the probability of a grain landing there. P(out)=3/4 simply means that the the portion of the base (circle) outside the triangle must be 3/4 of the are of the base.
_________________
Intern
Joined: 25 Apr 2013
Posts: 5
Location: India
Concentration: Strategy, Marketing
GPA: 2.7
WE: Information Technology (Computer Software)
Followers: 0

Kudos [?]: 5 [0], given: 4

Re: A cylindrical tank has a base with a circumference of [#permalink]  11 Jun 2013, 07:29
Hi,

Let P(E) = Probability of grain landing inside triangle = 1 - 3/4 = 1/4;--------(1)
Also P(E) = Area of Equilateral Triangle/Area of Base(i.e. Circle) ---------- (2)

Area (Triangle) = (3^1/2 / 4 )*a^2
Area (Circle) = pi*r^2 = pi * (2(3^1/2/pi)^1/2)^2 = 4*3^1/2

By using 1 & 2

a = 4 (Ans.)

Thanks & Regards,
Prateek Sharma
GMAT Club team member
Joined: 02 Sep 2009
Posts: 12116
Followers: 1879

Kudos [?]: 10135 [0], given: 965

Re: A cylindrical tank has a base with a circumference of [#permalink]  11 Jun 2013, 08:35
pratsh123 wrote:
Hi,

Let P(E) = Probability of grain landing inside triangle = 1 - 3/4 = 1/4;--------(1)
Also P(E) = Area of Equilateral Triangle/Area of Base(i.e. Circle) ---------- (2)

Area (Triangle) = (3^1/2 / 4 )*a^2
Area (Circle) = pi*r^2 = pi * (2(3^1/2/pi)^1/2)^2 = 4*3^1/2

By using 1 & 2

a = 4 (Ans.)

Thanks & Regards,
Prateek Sharma

a=2. Check here: a-cylindrical-tank-has-a-base-with-a-circumference-of-105453.html#p824188
_________________
Re: A cylindrical tank has a base with a circumference of   [#permalink] 11 Jun 2013, 08:35
Similar topics Replies Last post
Similar
Topics:
A cylindrical tank has a base with a circumference of meters 2 17 Jul 2006, 18:11
A cylindrical tank has a base with a circumference of 5 05 Nov 2006, 00:28
A cylindrical tank has a base with a circumference of 8 01 Jul 2007, 10:11
1 cylindrical tank 9 29 Jun 2008, 21:59
A closed tank contains 36pi cubic ft of water and is filled 2 16 May 2006, 18:51
Display posts from previous: Sort by