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Updated on: 04 Mar 2013, 12:02
Originally posted by bhandariavi on 26 Mar 2011, 12:14.
Last edited by Bunuel on 04 Mar 2013, 12:02, edited 1 time in total.
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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B
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Difficulty:
75%
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Question Stats:
55% (02:53) correct
45%
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wrong
based on 118
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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
A. 60 cm^3
B. 65 cm^3
C. 70 cm^3
D. 75 cm^3
E. 80 cm^3
26 Mar 2011, 12:40
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bhandariavi
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
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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disks_in_a_box.PNG [ 5.73 KiB | Viewed 4399 times ]
26 Mar 2011, 12:42
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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
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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