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

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13 disc-shaped objects (height 12/13 cm) are to be stacked [#permalink] New post 26 Mar 2011, 11:14
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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

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Last edited by Bunuel on 04 Mar 2013, 11:02, edited 1 time in total.
Renamed the topic and edited the question.
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Re: Try this one -- I didnt get the question [#permalink] New post 26 Mar 2011, 11:40
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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"
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Re: 13 disc-shaped objects (height 12/13 cm) are to be stacked [#permalink] New post 21 Sep 2013, 02:24
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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 :roll: ]


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.
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Re: Try this one -- I didnt get the question [#permalink] New post 26 Mar 2011, 11:42
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
Hence answer B
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Re: Try this one -- I didnt get the question [#permalink] New post 26 Mar 2011, 19:05
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

Answer - B
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Re: Try this one -- I didnt get the question [#permalink] New post 26 Mar 2011, 20:18
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"

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Cylinders : just couldnot understand the question [#permalink] New post 04 Mar 2013, 06:27
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
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Re: Cylinders : just couldnot understand the question [#permalink] New post 04 Mar 2013, 07:12
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

So, answer will be B
Hope it helps!
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Re: Cylinders : just couldnot understand the question [#permalink] New post 04 Mar 2013, 07:27
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

So, answer will be B
Hope it helps!


That was pretty obvious and easier than I thought :cry:

Nevertheless, thanks for awesome explanation..
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Re: Cylinders : just couldnot understand the question [#permalink] New post 04 Mar 2013, 11:03
Expert's post
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.

P.S. Please read and follow: rules-for-posting-please-read-this-before-posting-133935.html Thank you.
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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.


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Re: 13 disc-shaped objects (height 12/13 cm) are to be stacked [#permalink] New post 20 Sep 2013, 17:19
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 :roll: ]
Re: 13 disc-shaped objects (height 12/13 cm) are to be stacked   [#permalink] 20 Sep 2013, 17:19
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