It is currently 22 Nov 2017, 17:37

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

# 13 disc-shaped objects (height 12/13 cm) are to be stacked

Author Message
TAGS:

### Hide Tags

Manager
Joined: 04 Apr 2010
Posts: 159

Kudos [?]: 229 [0], given: 31

13 disc-shaped objects (height 12/13 cm) are to be stacked [#permalink]

### Show Tags

26 Mar 2011, 12:14
4
This post was
BOOKMARKED
00:00

Difficulty:

65% (hard)

Question Stats:

65% (02:34) correct 35% (02:41) wrong based on 86 sessions

### HideShow timer Statistics

13 disc-shaped objects (height 12/13 cm) are to be stacked in a rectangular box with horizontal dimensions (5 x 5cm). If the edges of the box contact the edges of the stack (so that there are no extra gaps) and the height of the stack and the box are exactly equal, approximately how much fluid gel can be injected into the remaining space?

A. 60 cm^3
B. 65 cm^3
C. 70 cm^3
D. 75 cm^3
E. 80 cm^3
[Reveal] Spoiler: OA

_________________

Consider me giving KUDOS, if you find my post helpful.
If at first you don't succeed, you're running about average. ~Anonymous

Last edited by Bunuel on 04 Mar 2013, 12:02, edited 1 time in total.
Renamed the topic and edited the question.

Kudos [?]: 229 [0], given: 31

Math Forum Moderator
Joined: 20 Dec 2010
Posts: 1965

Kudos [?]: 2097 [1], given: 376

Re: Try this one -- I didnt get the question [#permalink]

### Show Tags

26 Mar 2011, 12:40
1
KUDOS
bhandariavi wrote:
13 disc-shaped objects (height 12/13 cm) are to be stacked in a rectangular box with horizontal dimensions (5 x 5cm). If the edges of the box contact the edges of the stack (so that there are no extra gaps) and the height of the stack and the box are exactly equal, approximately how much fluid gel can be injected into the remaining space?

A 60cm3

B 65cm3

C 70cm3

D 75cm3

E 80cm3

It is a cylinder inserted in a rectangular box.

Dimension of the rectangular box:
l=5
w=5
h=13*(12/13)=12
Total Volume = l*b*h = 25*12

Dimension of the inserted cylinder:
r = (5/2). Please see the attached image providing a top view of the box. As the lateral edges of the box touch the circle and appear as tangent to the circle. The length and width of the rectangle become equal to diameter of the circle.

h = 13*(12/13)=12
Volume occupied $$\pi*r^2*h = \frac{22}{7}*(\frac{5}{2})^2*12= \frac{22}{7}*\frac{25}{4}*12$$

Volume left for the gel = Total Volume of the box - Volume occupied by cylinder

$$25*12 - \frac{22}{7}*\frac{25}{4}*12 = 25*12(1-\frac{22}{28})$$

$$25*12*\frac{6}{28}=\frac{450}{7}=64.2 \approx 65$$

Ans: "B"
Attachments

disks_in_a_box.PNG [ 5.73 KiB | Viewed 2280 times ]

_________________

Kudos [?]: 2097 [1], given: 376

Math Expert
Joined: 02 Sep 2009
Posts: 42305

Kudos [?]: 133073 [1], given: 12403

Re: 13 disc-shaped objects (height 12/13 cm) are to be stacked [#permalink]

### Show Tags

21 Sep 2013, 03:24
1
KUDOS
Expert's post
dixjatin wrote:
bhandariavi wrote:
13 disc-shaped objects (height 12/13 cm) are to be stacked in a rectangular box with horizontal dimensions (5 x 5cm). If the edges of the box contact the edges of the stack (so that there are no extra gaps) and the height of the stack and the box are exactly equal, approximately how much fluid gel can be injected into the remaining space?

A. 60 cm^3
B. 65 cm^3
C. 70 cm^3
D. 75 cm^3
E. 80 cm^3

The only problem I see in all the Explanations is that they assume that cylinders are stacked one above each other inside the box and not next to each other inside the box. [does stack means one above another ]

From the stem we can get that the discs are placed exactly the way explained in the solutions: the discs are to be stacked in a rectangular box with horizontal dimensions (5 x 5cm). If the edges of the box contact the edges of the stack (so that there are no extra gaps) and the height of the stack and the box are exactly equal.
_________________

Kudos [?]: 133073 [1], given: 12403

Manager
Joined: 07 Oct 2010
Posts: 174

Kudos [?]: 179 [0], given: 10

Re: Try this one -- I didnt get the question [#permalink]

### Show Tags

26 Mar 2011, 12:42
There are 13 discs shaped objects and hight of one object is 12/13
Therefore, total hight will be 13* 12/13 = 12cm

Now ht of box = ht of the stack

Therefore, Volume of the box = lbh = 5 * 5 * 12 = 25 * 12

Now, volume of the stack = $$πr^2h$$ = 22/7 * 6.25 * 12 = approximately 19.5 * 12

Now take the difference between two
i. e. 25*12 - 19.5*12 = 12 (25 - 19.5) = 12 * 5.5 = 66cm

Therefore, approximate space in which the gel can be filled will be 65cm

Kudos [?]: 179 [0], given: 10

TOEFL Forum Moderator
Joined: 16 Nov 2010
Posts: 1603

Kudos [?]: 601 [0], given: 40

Location: United States (IN)
Concentration: Strategy, Technology
Re: Try this one -- I didnt get the question [#permalink]

### Show Tags

26 Mar 2011, 20:05
Volume of box = 5 * 5 * (12/13) * 13

= 25 * 12

Volume of Discs in a cylindrical shape = pi * (5/2)^2 * 12/13 * 13

= pi * 25/4 * 12

= pi * 25 * 3

So volume of gel that can be injected = 25 ( 12 - 3pi)

= 25 (12 - 9.42)

= 25 * 2.58

= 64.5 cm^3

_________________

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

GMAT Club Premium Membership - big benefits and savings

Kudos [?]: 601 [0], given: 40

Manager
Joined: 04 Apr 2010
Posts: 159

Kudos [?]: 229 [0], given: 31

Re: Try this one -- I didnt get the question [#permalink]

### Show Tags

26 Mar 2011, 21:18
fluke wrote:
bhandariavi wrote:
13 disc-shaped objects (height 12/13 cm) are to be stacked in a rectangular box with horizontal dimensions (5 x 5cm). If the edges of the box contact the edges of the stack (so that there are no extra gaps) and the height of the stack and the box are exactly equal, approximately how much fluid gel can be injected into the remaining space?

A 60cm3

B 65cm3

C 70cm3

D 75cm3

E 80cm3

It is a cylinder inserted in a rectangular box.

Dimension of the rectangular box:
l=5
w=5
h=13*(12/13)=12
Total Volume = l*b*h = 25*12

Dimension of the inserted cylinder:
r = (5/2). Please see the attached image providing a top view of the box. As the lateral edges of the box touch the circle and appear as tangent to the circle. The length and width of the rectangle become equal to diameter of the circle.

h = 13*(12/13)=12
Volume occupied $$\pi*r^2*h = \frac{22}{7}*(\frac{5}{2})^2*12= \frac{22}{7}*\frac{25}{4}*12$$

Volume left for the gel = Total Volume of the box - Volume occupied by cylinder

$$25*12 - \frac{22}{7}*\frac{25}{4}*12 = 25*12(1-\frac{22}{28})$$

$$25*12*\frac{6}{28}=\frac{450}{7}=64.2 \approx 65$$

Ans: "B"

Great Job Fluke +1 for you.
_________________

Consider me giving KUDOS, if you find my post helpful.
If at first you don't succeed, you're running about average. ~Anonymous

Kudos [?]: 229 [0], given: 31

Manager
Joined: 04 Sep 2012
Posts: 141

Kudos [?]: 77 [0], given: 27

Cylinders : just couldnot understand the question [#permalink]

### Show Tags

04 Mar 2013, 07:27
13 disc-shaped objects (height 12/13 cm) are to be stacked in a rectangular box with horizontal dimensions (5 x 5cm). If the edges of the box contact the edges of the stack (so that there are no extra gaps) and the height of the stack and the box are exactly equal, approximately how much fluid gel can be injected into the remaining space?

A.60 cm^3
B.65 cm^3
C.70 cm^3
D.75 cm^3
E.80 cm^3
_________________

Regards,
Abhinav

GMAT 1 - 580 (Q47 V23) http://gmatclub.com/forum/a-tight-slap-on-face-149457.html

GMAT 2 - 670 (Q48 V34) http://gmatclub.com/forum/670-one-month-off-from-office-and-2-months-hard-work-163761.html#p1297561

Kudos [?]: 77 [0], given: 27

Director
Status: Tutor - BrushMyQuant
Joined: 05 Apr 2011
Posts: 617

Kudos [?]: 798 [0], given: 59

Location: India
Concentration: Finance, Marketing
Schools: XLRI (A)
GMAT 1: 700 Q51 V31
GPA: 3
WE: Information Technology (Computer Software)
Re: Cylinders : just couldnot understand the question [#permalink]

### Show Tags

04 Mar 2013, 08:12
abhinav11 wrote:
13 disc-shaped objects (height 12/13 cm) are to be stacked in a rectangular box with horizontal dimensions (5 x 5cm). If the edges of the box contact the edges of the stack (so that there are no extra gaps) and the height of the stack and the box are exactly equal, approximately how much fluid gel can be injected into the remaining space?

A.60 cm^3
B.65 cm^3
C.70 cm^3
D.75 cm^3
E.80 cm^3

Question is saying that there is a rectangle box in which we have to fit 13 disc shaped object
-> those thirteen on top of each other will eventually make a cylinder of height 13 * 12/13 and diameter = 5cm

Now imagine a rectangular 3D box and a cylinder inside it. There will be some space left as cylinder is curved around its edge. So, we need to find how much is that space.
So, that space will be volume of the rectangular box - volume of the cylinder

= (5 * 5 * 12) - (pie ((5/2)^2) * 12)
= 300 - 235.5
= 64.5 cm^3

Hope it helps!
_________________

Ankit

Check my Tutoring Site -> Brush My Quant

GMAT Quant Tutor
How to start GMAT preparations?
How to Improve Quant Score?
Gmatclub Topic Tags
Check out my GMAT debrief

How to Solve :
Statistics || Reflection of a line || Remainder Problems || Inequalities

Kudos [?]: 798 [0], given: 59

Manager
Joined: 04 Sep 2012
Posts: 141

Kudos [?]: 77 [0], given: 27

Re: Cylinders : just couldnot understand the question [#permalink]

### Show Tags

04 Mar 2013, 08:27
nktdotgupta wrote:
abhinav11 wrote:
13 disc-shaped objects (height 12/13 cm) are to be stacked in a rectangular box with horizontal dimensions (5 x 5cm). If the edges of the box contact the edges of the stack (so that there are no extra gaps) and the height of the stack and the box are exactly equal, approximately how much fluid gel can be injected into the remaining space?

A.60 cm^3
B.65 cm^3
C.70 cm^3
D.75 cm^3
E.80 cm^3

Question is saying that there is a rectangle box in which we have to fit 13 disc shaped object
-> those thirteen on top of each other will eventually make a cylinder of height 13 * 12/13 and diameter = 5cm

Now imagine a rectangular 3D box and a cylinder inside it. There will be some space left as cylinder is curved around its edge. So, we need to find how much is that space.
So, that space will be volume of the rectangular box - volume of the cylinder

= (5 * 5 * 12) - (pie ((5/2)^2) * 12)
= 300 - 235.5
= 64.5 cm^3

Hope it helps!

That was pretty obvious and easier than I thought

Nevertheless, thanks for awesome explanation..
_________________

Regards,
Abhinav

GMAT 1 - 580 (Q47 V23) http://gmatclub.com/forum/a-tight-slap-on-face-149457.html

GMAT 2 - 670 (Q48 V34) http://gmatclub.com/forum/670-one-month-off-from-office-and-2-months-hard-work-163761.html#p1297561

Kudos [?]: 77 [0], given: 27

Math Expert
Joined: 02 Sep 2009
Posts: 42305

Kudos [?]: 133073 [0], given: 12403

Re: Cylinders : just couldnot understand the question [#permalink]

### Show Tags

04 Mar 2013, 12:03
abhinav11 wrote:
13 disc-shaped objects (height 12/13 cm) are to be stacked in a rectangular box with horizontal dimensions (5 x 5cm). If the edges of the box contact the edges of the stack (so that there are no extra gaps) and the height of the stack and the box are exactly equal, approximately how much fluid gel can be injected into the remaining space?

A.60 cm^3
B.65 cm^3
C.70 cm^3
D.75 cm^3
E.80 cm^3

Merging similar topics.

_________________

Kudos [?]: 133073 [0], given: 12403

Intern
Joined: 25 Jul 2012
Posts: 6

Kudos [?]: 7 [0], given: 10

Re: 13 disc-shaped objects (height 12/13 cm) are to be stacked [#permalink]

### Show Tags

20 Sep 2013, 18:19
bhandariavi wrote:
13 disc-shaped objects (height 12/13 cm) are to be stacked in a rectangular box with horizontal dimensions (5 x 5cm). If the edges of the box contact the edges of the stack (so that there are no extra gaps) and the height of the stack and the box are exactly equal, approximately how much fluid gel can be injected into the remaining space?

A. 60 cm^3
B. 65 cm^3
C. 70 cm^3
D. 75 cm^3
E. 80 cm^3

The only problem I see in all the Explanations is that they assume that cylinders are stacked one above each other inside the box and not next to each other inside the box. [does stack means one above another ]

Kudos [?]: 7 [0], given: 10

Non-Human User
Joined: 09 Sep 2013
Posts: 15546

Kudos [?]: 283 [0], given: 0

Re: 13 disc-shaped objects (height 12/13 cm) are to be stacked [#permalink]

### Show Tags

15 May 2017, 03:11
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________

Kudos [?]: 283 [0], given: 0

Re: 13 disc-shaped objects (height 12/13 cm) are to be stacked   [#permalink] 15 May 2017, 03:11
Display posts from previous: Sort by