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655-705 (Hard)|   Geometry|      
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Bunuel
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On the outside, a closed rectangular packing box, made out of cardboar 27 Nov 2018, 00:35
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D
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61% (02:29) correct 39% (02:26) wrong based on 154 sessions

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On the outside, a closed rectangular packing box, made out of cardboard, is 12 inches long, 18 inches wide, and 24 inches high. If the cardboard is 1/4 inch thick, which of the following is closest to the volume inside the box, in cubic inches?

A. 3,700
B. 3,900
C. 4,300
D. 4,700
E. 5,200
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D
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On the outside, a closed rectangular packing box, made out of cardboar Updated on: 28 Nov 2018, 07:04
Originally posted by Archit3110 on 27 Nov 2018, 11:06.
Last edited by Archit3110 on 28 Nov 2018, 07:04, edited 1 time in total.
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Bunuel
On the outside, a closed rectangular packing box, made out of cardboard, is 12 inches long, 18 inches wide, and 24 inches high. If the cardboard is 1/4 inch thick, which of the following is closest to the volume inside the box, in cubic inches?

A. 3,700
B. 3,900
C. 4,300
D. 4,700
E. 5,200
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total volume 12* 18*24 = ~ 5184

thickness is 1/4 so 5184*1/4= 1296

0.25 thickness will reduce the dimensions if each side : 11.75*17.75*23.75 =~4900
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On the outside, a closed rectangular packing box, made out of cardboar 28 Nov 2018, 06:34
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Bunuel
On the outside, a closed rectangular packing box, made out of cardboard, is 12 inches long, 18 inches wide, and 24 inches high. If the cardboard is 1/4 inch thick, which of the following is closest to the volume inside the box, in cubic inches?

A. 3,700
B. 3,900
C. 4,300
D. 4,700
E. 5,200
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Original Dimensions are 12,18,24. Hence Original Volume is lbh = 18*12*24 = 5184

Thickness is 1/4th inch or 0.25 inches.

New Dimensions are 11.75, 17.75, 23.75. Hence new volume is 11.75*17.75*23.75 = 4954.
Closest value to this figure is option (d).

Is there any faster way to do this?
The calculations got a little complex with the decimals.
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On the outside, a closed rectangular packing box, made out of cardboar 29 Nov 2018, 08:41
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ParthSanghavi
Bunuel
On the outside, a closed rectangular packing box, made out of cardboard, is 12 inches long, 18 inches wide, and 24 inches high. If the cardboard is 1/4 inch thick, which of the following is closest to the volume inside the box, in cubic inches?

A. 3,700
B. 3,900
C. 4,300
D. 4,700
E. 5,200


Original Dimensions are 12,18,24. Hence Original Volume is lbh = 18*12*24 = 5184

Thickness is 1/4th inch or 0.25 inches.

New Dimensions are 11.75, 17.75, 23.75. Hence new volume is 11.75*17.75*23.75 = 4954.
Closest value to this figure is option (d).

Is there any faster way to do this?
The calculations got a little complex with the decimals.
Show more


I thought of it the same way, and by calculator it was closer to D. However, it's about thickness not length of the dimension. It is 1/4 inch all across each of the dimension, and the above answer reduces the dimensions by .25 inch
I'm not sure what is the method and request Bunuel to please advise.
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On the outside, a closed rectangular packing box, made out of cardboar 29 Nov 2018, 09:32
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Hi,

I think easiest way to solve this problem is:

volume of the box = 18*12*24 ----> 18*12*12*2 ---> 18*144*2 --->18*288-->(20-2)*288 --->5184.
so, E is out. It could be either C or D. To decide between C and D. Suppose we reduce the dimensions by 1 inch from all the sides. volume will be
17*11*23 -->(20-3)*23*11 --->391*11-->4301. C is out. so definitely it is D.

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On the outside, a closed rectangular packing box, made out of cardboar 09 Dec 2018, 19:16
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my approach
As thickness of the cardboard around the rectangular box ,
subtracted 2*.25 from each dimension
11.5*17.5*23.5 = 4729 (approximately)- Ans D
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On the outside, a closed rectangular packing box, made out of cardboar 10 Dec 2018, 00:20
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V - dV = 12*18*24 - 1/2*18*24 - 12*(1/2)*24 - 12*18*(1/2) = 5184 - 468 = 4716

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On the outside, a closed rectangular packing box, made out of cardboar 10 Dec 2018, 09:46
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the answer should be bigger than 11x17x23 but smaller than 12x18x24.

11x17x23 = 4304
12x18x24 = 5184

only D is possible
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On the outside, a closed rectangular packing box, made out of cardboar 09 Nov 2019, 12:29
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There is another approach. every side is counted twice, so thickness we need to double for each side and solve:
(12 - 2x1/4)x(18 - 2x1/4)x(24 - 2x1/4)=11,5x17,5x23,5=4729,4

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On the outside, a closed rectangular packing box, made out of cardboar 21 Nov 2020, 00:09
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The inner dimensions of the cuboid will be 11.5 [12-(2*0.25)] x 17.5 [18-(2*0.25)] x 23.5 [24-(2*0.25)].
Thus the area would 11.5x17.5x23.5 ~4500
None of the answer matches.
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On the outside, a closed rectangular packing box, made out of cardboar 25 Jul 2025, 12:11
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