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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]

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26 Mar 2011, 12:14
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Question Stats:

64% (03:35) correct 36% (02:41) wrong based on 84 sessions

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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, 12:02, 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]

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26 Mar 2011, 12:40
1
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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]

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21 Sep 2013, 03:24
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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.
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Re: Try this one -- I didnt get the question [#permalink]

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

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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

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Manager
Joined: 04 Apr 2010
Posts: 162
Re: Try this one -- I didnt get the question [#permalink]

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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.
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Manager
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Posts: 142
Cylinders : just couldnot understand the question [#permalink]

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

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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!
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Manager
Joined: 04 Sep 2012
Posts: 142
Re: Cylinders : just couldnot understand the question [#permalink]

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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..
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Abhinav

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Posts: 39622
Re: Cylinders : just couldnot understand the question [#permalink]

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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.

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Posts: 7
Re: 13 disc-shaped objects (height 12/13 cm) are to be stacked [#permalink]

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

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