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# A 2-foot by 2-foot by 2-foot solid cube is cut into 2-inch by 2-inch

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Math Expert
Joined: 02 Sep 2009
Posts: 55277
A 2-foot by 2-foot by 2-foot solid cube is cut into 2-inch by 2-inch  [#permalink]

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17 Sep 2018, 01:42
00:00

Difficulty:

45% (medium)

Question Stats:

45% (02:12) correct 55% (02:36) wrong based on 16 sessions

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A 2-foot by 2-foot by 2-foot solid cube is cut into 2-inch by 2-inch by 4-inch rectangular solids. What is the ratio of the total surface area of all the resulting smaller rectangular solids to the surface area of the original cube? (1 foot = 12 inches)

(A) 2 : 1
(B) 4 : 1
(C) 5 : 1
(D) 8 : 1
(E) 10 : 1

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A 2-foot by 2-foot by 2-foot solid cube is cut into 2-inch by 2-inch  [#permalink]

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Updated on: 17 Sep 2018, 11:46
Bunuel wrote:
A 2-foot by 2-foot by 2-foot solid cube is cut into 2-inch by 2-inch by 4-inch rectangular solids. What is the ratio of the total surface area of all the resulting smaller rectangular solids to the surface area of the original cube? (1 foot = 12 inches)

(A) 2 : 1
(B) 4 : 1
(C) 5 : 1
(D) 8 : 1
(E) 10 : 1

volume of the larger cube = n * volume of smaller cubes (where n is the total number of cubes)

24*24*24 = n * 2*2*4
n=24*12*3
ratio => $$\frac{24*12*3*6*2(8+8+4)}{6*24*24*12}$$ = 10/1

Originally posted by CounterSniper on 17 Sep 2018, 08:41.
Last edited by CounterSniper on 17 Sep 2018, 11:46, edited 1 time in total.
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Joined: 14 Sep 2018
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Re: A 2-foot by 2-foot by 2-foot solid cube is cut into 2-inch by 2-inch  [#permalink]

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17 Sep 2018, 08:58
Bunuel wrote:
A 2-foot by 2-foot by 2-foot solid cube is cut into 2-inch by 2-inch by 4-inch rectangular solids. What is the ratio of the total surface area of all the resulting smaller rectangular solids to the surface area of the original cube? (1 foot = 12 inches)

(A) 2 : 1
(B) 4 : 1
(C) 5 : 1
(D) 8 : 1
(E) 10 : 1

here it is a matter of surface area. so Ans will be 10:1 so E
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Re: A 2-foot by 2-foot by 2-foot solid cube is cut into 2-inch by 2-inch  [#permalink]

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17 Sep 2018, 09:45
Bunuel wrote:
A 2-foot by 2-foot by 2-foot solid cube is cut into 2-inch by 2-inch by 4-inch rectangular solids. What is the ratio of the total surface area of all the resulting smaller rectangular solids to the surface area of the original cube? (1 foot = 12 inches)

(A) 2 : 1
(B) 4 : 1
(C) 5 : 1
(D) 8 : 1
(E) 10 : 1

E.

total number of boxes cut = (24*24*24)/(2*2*4) = 864
area of 1 box = 2[4+8+8] = 40
area of all boxes = 40*864
area of cube = 6*24*24
ratio = 10:1
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Re: A 2-foot by 2-foot by 2-foot solid cube is cut into 2-inch by 2-inch   [#permalink] 17 Sep 2018, 09:45
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