Author 
Message 
TAGS:

Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 43916

A container in the shape of a right circular cylinder is 1/2 [#permalink]
Show Tags
16 Jul 2012, 03:40
Question Stats:
79% (01:32) correct 21% (01:40) wrong based on 1020 sessions
HideShow timer Statistics



Math Expert
Joined: 02 Sep 2009
Posts: 43916

Re: A container in the shape of a right circular cylinder is 1/2 [#permalink]
Show Tags
16 Jul 2012, 12:07
2
This post received KUDOS
Expert's post
5
This post was BOOKMARKED
SOLUTIONA container in the shape of a right circular cylinder is 1/2 full of water. If the volume of water in the container is 36 cubic inches and the height of the container is 9 inches, what is the diameter of the base of the cylinder, in inches?(A) \(\frac{16}{9\pi}\) (B) \(\frac{4}{\pi}\) (C) \(\frac{12}{\pi}\) (D) \(\sqrt{\frac{2}{\pi}}\) (E) \(4\sqrt{\frac{2}{\pi}}\) Since 36 cubic inches of water occupy 1/2 of the cylinder, then the volume of the cylinder is 72 cubic inches. So, we have that \(volume_{cylinder}=\pi*{r^2}*h=72\) > \(\pi*{r^2}*9=72\) > \(r^2=\frac{8}{\pi}\) > \(r=\sqrt{\frac{8}{\pi}}=2*\sqrt{\frac{2}{\pi}}\). Hence the diameter equals \(2*(2*\sqrt{\frac{2}{\pi}})=4*\sqrt{\frac{2}{\pi}}\). Answer: E. Hope it's clear.
_________________
New to the Math Forum? Please read this: Ultimate GMAT Quantitative Megathread  All You Need for Quant  PLEASE READ AND FOLLOW: 12 Rules for Posting!!! Resources: GMAT Math Book  Triangles  Polygons  Coordinate Geometry  Factorials  Circles  Number Theory  Remainders; 8. Overlapping Sets  PDF of Math Book; 10. Remainders  GMAT Prep Software Analysis  SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS)  Tricky questions from previous years.
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. ,11 Mixed Questions, 12 Fresh Meat 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., 11 New DS set.
What are GMAT Club Tests? Extrahard Quant Tests with Brilliant Analytics



Manager
Joined: 06 Jun 2012
Posts: 82
Concentration: Technology, Entrepreneurship

Re: A container in the shape of a right circular cylinder is 1/2 [#permalink]
Show Tags
16 Jul 2012, 12:26
the answer is E. The volume of the cylinder is = hr^2(Pie). If Half of the volume is equal to 36 than the full volume is 72. since h =9 divide 72/9(pie) u get r^2=8/Pie or r^2=(4*2)/pie. so r= 2*Sqrt(2/pie) Since 2r = diameter => diameter = 4*Sqrt(2/pie)
_________________
Try to make my way to San Jose.
??? class of 2016



Intern
Joined: 23 Oct 2012
Posts: 5

Re: A container in the shape of a right circular cylinder is 1/2 [#permalink]
Show Tags
29 Oct 2012, 02:46
Hi
Could someone simplify it. I don't get it.
What I understand so far is that the container is half full at 36 cubic = full 72 cubic Height of container is 9 inches = so container with half full is at 4.5 inches height...
72 = 9 36 = 4.5
after this I get stuck with the explanations that have been given....
Thanks



Math Expert
Joined: 02 Sep 2009
Posts: 43916

Re: A container in the shape of a right circular cylinder is 1/2 [#permalink]
Show Tags
29 Oct 2012, 02:52
DonCarter wrote: Hi
Could someone simplify it. I don't get it.
What I understand so far is that the container is half full at 36 cubic = full 72 cubic Height of container is 9 inches = so container with half full is at 4.5 inches height...
72 = 9 36 = 4.5
after this I get stuck with the explanations that have been given....
Thanks You don't need to for halffull container after you get that the volume of the whole container is 72 cubic inches. We have that the volume is 72 cubic inches and the height is 9 inches > \(volume_{cylinder}=\pi*{r^2}*h=72\) > \(\pi*{r^2}*9=72\) > \(r^2=\frac{8}{\pi}\) > \(r=\sqrt{\frac{8}{\pi}}=2*\sqrt{\frac{2}{\pi}}\). Hence the diameter equals \(2*(2*\sqrt{\frac{2}{\pi}})=4*\sqrt{\frac{2}{\pi}}\). Hope it's clear.
_________________
New to the Math Forum? Please read this: Ultimate GMAT Quantitative Megathread  All You Need for Quant  PLEASE READ AND FOLLOW: 12 Rules for Posting!!! Resources: GMAT Math Book  Triangles  Polygons  Coordinate Geometry  Factorials  Circles  Number Theory  Remainders; 8. Overlapping Sets  PDF of Math Book; 10. Remainders  GMAT Prep Software Analysis  SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS)  Tricky questions from previous years.
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. ,11 Mixed Questions, 12 Fresh Meat 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., 11 New DS set.
What are GMAT Club Tests? Extrahard Quant Tests with Brilliant Analytics



Math Expert
Joined: 02 Sep 2009
Posts: 43916

Re: A container in the shape of a right circular cylinder is 1/2 [#permalink]
Show Tags
29 Oct 2012, 04:49



Intern
Joined: 30 Apr 2013
Posts: 2

Re: A container in the shape of a right circular cylinder is 1/2 [#permalink]
Show Tags
15 May 2013, 07:45
How do you reach the square root of 8 over pie being = to 2 multiplied the square root of 2 over pie?



Math Expert
Joined: 02 Sep 2009
Posts: 43916

Re: A container in the shape of a right circular cylinder is 1/2 [#permalink]
Show Tags
15 May 2013, 07:47



Intern
Joined: 30 Apr 2013
Posts: 2

Re: A container in the shape of a right circular cylinder is 1/2 [#permalink]
Show Tags
15 May 2013, 07:56
Bunuel wrote: kck wrote: How do you reach the square root of 8 over pie being = to 2 multiplied the square root of 2 over pie? Welcome to the club! \(r=\sqrt{\frac{8}{\pi}}=\sqrt{\frac{4*2}{\pi}}=2*\sqrt{\frac{2}{\pi}}\). Does this make sense? Thank you for the welcome and yes it does! Now it seems so simple. Thanks again buddy!



Manager
Joined: 12 Jan 2013
Posts: 216

Re: A container in the shape of a right circular cylinder is 1/2 [#permalink]
Show Tags
17 Dec 2013, 08:55
Bunuel wrote: A container in the shape of a right circular cylinder is 1/2 full of water. If the volume of water in the container is 36 cubic inches and the height of the container is 9 inches, what is the diameter of the base of the cylinder, in inches? (A) \(\frac{16}{9\pi}\) (B) \(\frac{4}{\pi}\) (C) \(\frac{12}{\pi}\) (D) \(\sqrt{\frac{2}{\pi}}\) (E) \(4\sqrt{\frac{2}{\pi}}\) Diagnostic Test Question: 22 Page: 23 Difficulty: 600 They give us cubic inches > 36in^3 and then want us to find find a value that is in inches > in^1 .. Why are they not consistent? If they talk about cubic inches then they should also take the cubic root out on both sides... I don't get it.



Math Expert
Joined: 02 Sep 2009
Posts: 43916

Re: A container in the shape of a right circular cylinder is 1/2 [#permalink]
Show Tags
17 Dec 2013, 08:58
aeglorre wrote: Bunuel wrote: A container in the shape of a right circular cylinder is 1/2 full of water. If the volume of water in the container is 36 cubic inches and the height of the container is 9 inches, what is the diameter of the base of the cylinder, in inches? (A) \(\frac{16}{9\pi}\) (B) \(\frac{4}{\pi}\) (C) \(\frac{12}{\pi}\) (D) \(\sqrt{\frac{2}{\pi}}\) (E) \(4\sqrt{\frac{2}{\pi}}\) Diagnostic Test Question: 22 Page: 23 Difficulty: 600 They give us cubic inches > 36in^3 and then want us to find find a value that is in inches > in^1 .. Why are they not consistent? If they talk about cubic inches then they should also take the cubic root out on both sides... I don't get it. Volume is in cubic inches and the length is in inches. How can length be in cubic inches?
_________________
New to the Math Forum? Please read this: Ultimate GMAT Quantitative Megathread  All You Need for Quant  PLEASE READ AND FOLLOW: 12 Rules for Posting!!! Resources: GMAT Math Book  Triangles  Polygons  Coordinate Geometry  Factorials  Circles  Number Theory  Remainders; 8. Overlapping Sets  PDF of Math Book; 10. Remainders  GMAT Prep Software Analysis  SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS)  Tricky questions from previous years.
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. ,11 Mixed Questions, 12 Fresh Meat 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., 11 New DS set.
What are GMAT Club Tests? Extrahard Quant Tests with Brilliant Analytics



Manager
Joined: 12 Jan 2013
Posts: 216

Re: A container in the shape of a right circular cylinder is 1/2 [#permalink]
Show Tags
17 Dec 2013, 12:25
Bunuel wrote: aeglorre wrote: Bunuel wrote: A container in the shape of a right circular cylinder is 1/2 full of water. If the volume of water in the container is 36 cubic inches and the height of the container is 9 inches, what is the diameter of the base of the cylinder, in inches? (A) \(\frac{16}{9\pi}\) (B) \(\frac{4}{\pi}\) (C) \(\frac{12}{\pi}\) (D) \(\sqrt{\frac{2}{\pi}}\) (E) \(4\sqrt{\frac{2}{\pi}}\) Diagnostic Test Question: 22 Page: 23 Difficulty: 600 They give us cubic inches > 36in^3 and then want us to find find a value that is in inches > in^1 .. Why are they not consistent? If they talk about cubic inches then they should also take the cubic root out on both sides... I don't get it. Volume is in cubic inches and the length is in inches. How can length be in cubic inches? Wow, that is embarassing. Thanks for the heads up, Ill just blame it on mind fatigue!



Senior Manager
Joined: 13 May 2013
Posts: 456

Re: A container in the shape of a right circular cylinder is 1/2 [#permalink]
Show Tags
17 Dec 2013, 13:01
A container in the shape of a right circular cylinder is 1/2 full of water. If the volume of water in the container is 36 cubic inches and the height of the container is 9 inches, what is the diameter of the base of the cylinder, in inches?I've gotten this question wrong before and I'm still not 100% sure why it's solved the way it is. If the container is 1/2 full of water and the volume of water is 36 when the total volume is twice that, or 72 inches. V = pi * r^2 * h 72 = pi * r^2 * (9) 8 = pi * r^2 8/pi = r^2 √8 / √pi = r d = 2r d = 2(√8 / √pi) d = 2√8 / √pi d = (2 * √8 * √pi) / pi



Math Expert
Joined: 02 Sep 2009
Posts: 43916

Re: A container in the shape of a right circular cylinder is 1/2 [#permalink]
Show Tags
18 Dec 2013, 00:59
WholeLottaLove wrote: A container in the shape of a right circular cylinder is 1/2 full of water. If the volume of water in the container is 36 cubic inches and the height of the container is 9 inches, what is the diameter of the base of the cylinder, in inches?I've gotten this question wrong before and I'm still not 100% sure why it's solved the way it is. If the container is 1/2 full of water and the volume of water is 36 when the total volume is twice that, or 72 inches. V = pi * r^2 * h 72 = pi * r^2 * (9) 8 = pi * r^2 8/pi = r^2 √8 / √pi = rd = 2r d = 2(√8 / √pi) d = 2√8 / √pi d = (2 * √8 * √pi) / pi The red part can simplified: \(r=\sqrt{\frac{8}{\pi}}=\sqrt{\frac{4*2}{\pi}}=2*\sqrt{\frac{2}{\pi}}\).
_________________
New to the Math Forum? Please read this: Ultimate GMAT Quantitative Megathread  All You Need for Quant  PLEASE READ AND FOLLOW: 12 Rules for Posting!!! Resources: GMAT Math Book  Triangles  Polygons  Coordinate Geometry  Factorials  Circles  Number Theory  Remainders; 8. Overlapping Sets  PDF of Math Book; 10. Remainders  GMAT Prep Software Analysis  SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS)  Tricky questions from previous years.
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. ,11 Mixed Questions, 12 Fresh Meat 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., 11 New DS set.
What are GMAT Club Tests? Extrahard Quant Tests with Brilliant Analytics



Senior Manager
Joined: 13 May 2013
Posts: 456

Re: A container in the shape of a right circular cylinder is 1/2 [#permalink]
Show Tags
18 Dec 2013, 14:49
Ahh...simple mistake! Thanks! quote="Bunuel"] WholeLottaLove wrote: A container in the shape of a right circular cylinder is 1/2 full of water. If the volume of water in the container is 36 cubic inches and the height of the container is 9 inches, what is the diameter of the base of the cylinder, in inches?I've gotten this question wrong before and I'm still not 100% sure why it's solved the way it is. If the container is 1/2 full of water and the volume of water is 36 when the total volume is twice that, or 72 inches. V = pi * r^2 * h 72 = pi * r^2 * (9) 8 = pi * r^2 8/pi = r^2 √8 / √pi = rd = 2r d = 2(√8 / √pi) d = 2√8 / √pi d = (2 * √8 * √pi) / pi The red part can simplified: \(r=\sqrt{\frac{8}{\pi}}=\sqrt{\frac{4*2}{\pi}}=2*\sqrt{\frac{2}{\pi}}\).[/quote]



Manager
Joined: 15 Aug 2013
Posts: 58

Re: A container in the shape of a right circular cylinder is 1/2 [#permalink]
Show Tags
19 Dec 2013, 03:14
I understand how it is done above. But can someone help me explain what is wrong with below  Given is a right circular cylinder, which is half full. V/2 = 36. Also height will be half i.e. 4.5 inches when the culinder is half full. Hence, (pi*r^2*4.5)/2 = 36. This gives radius = 4/sqrt(pi). This is wrong though.
I am not quite sure what is wrong with this. Can someone explain ?



Math Expert
Joined: 02 Sep 2009
Posts: 43916

Re: A container in the shape of a right circular cylinder is 1/2 [#permalink]
Show Tags
19 Dec 2013, 03:23



Target Test Prep Representative
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 2192
Location: United States (CA)

Re: A container in the shape of a right circular cylinder is 1/2 [#permalink]
Show Tags
21 Jan 2018, 19:02
Bunuel wrote: A container in the shape of a right circular cylinder is 1/2 full of water. If the volume of water in the container is 36 cubic inches and the height of the container is 9 inches, what is the diameter of the base of the cylinder, in inches?
(A) \(\frac{16}{9\pi}\)
(B) \(\frac{4}{\pi}\)
(C) \(\frac{12}{\pi}\)
(D) \(\sqrt{\frac{2}{\pi}}\)
(E) \(4\sqrt{\frac{2}{\pi}}\) Recall that the volume of a cylinder is: volume = π(radius)^2(height) Since half of the capacity of the cylinder is 36, the full capacity of the cylinder is 72; thus: 72 = πr^2(9) 8/π = r^2 √(8/π) = r √8/√π = r (2√2)/√π = r 2√(2/π) = r The diameter is twice the radius. Thus, the diameter is 2 x 2√(2/π) = 4√(2/π). Answer: E
_________________
Scott WoodburyStewart
Founder and CEO
GMAT Quant SelfStudy Course
500+ lessons 3000+ practice problems 800+ HD solutions




Re: A container in the shape of a right circular cylinder is 1/2
[#permalink]
21 Jan 2018, 19:02






