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A 2-foot by 2-foot by 2-foot solid cube is cut into 2-inch b
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14 Sep 2018, 16:32
14 Sep 2018, 16:32
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Question Stats:
63% (02:51) correct
36% (02:45) wrong based on 60 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
(A) 2 : 1
(B) 4 : 1
(C) 5 : 1
(D) 8 : 1
(E) 10 : 1
Re: A 2-foot by 2-foot by 2-foot solid cube is cut into 2-inch b
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15 Sep 2019, 13:35
15 Sep 2019, 13:35
sandy 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
(A) 2 : 1
(B) 4 : 1
(C) 5 : 1
(D) 8 : 1
(E) 10 : 1
Need an Explanation.
Re: A 2-foot by 2-foot by 2-foot solid cube is cut into 2-inch b
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15 Sep 2019, 15:49
15 Sep 2019, 15:49
Expert Reply
This is a really time-consuming question. It is tricky. However, the real GRE questions are ,yes, time-consuming but they have also always some sort of short cut that once you get the question, then it is easy.
This is only time-consuming and stop.
Now, to have the area of the original cube you have to take into account that the area is \(6 \times s^2\)
You do need to convert one side which is 2 inches in feet or the other way around.
2 feet = 24 inches
Area is \(6 \times (24)^2 = 3,456\) square inches
Each large solid is \(24 \times 24 \times 24\).
To have the smal rectangular solid you have to slice the large cube into smaller cubes which have the measure of 2-inches \(\times\) 2 inches \(\ times\) 4 inch
so, \(\frac{24}{2} \times \frac{24}{2} \times \frac{24}{4} = 864\) smal cubes from the large one.
Now we do need to calculate the surface area of the small on in order to know the total numbers of the smaller ones to calculate the ratio
\(2lw + 2wh+2lh = 2 (2 \times 2 ) + 2 (2 \times 4 ) + 2 (2 \times 4 ) = 40\) square inches per smal rectangular solid.
\(40 \times 864 = 34,560\) square inches
the ratio is \(\frac{34,560}{3,456} = \frac{10}{1}\)
E is the answer.
PS: again, this is NOT a question you will ever meet during the real GRE
This is only time-consuming and stop.
Now, to have the area of the original cube you have to take into account that the area is \(6 \times s^2\)
You do need to convert one side which is 2 inches in feet or the other way around.
2 feet = 24 inches
Area is \(6 \times (24)^2 = 3,456\) square inches
Each large solid is \(24 \times 24 \times 24\).
To have the smal rectangular solid you have to slice the large cube into smaller cubes which have the measure of 2-inches \(\times\) 2 inches \(\ times\) 4 inch
so, \(\frac{24}{2} \times \frac{24}{2} \times \frac{24}{4} = 864\) smal cubes from the large one.
Now we do need to calculate the surface area of the small on in order to know the total numbers of the smaller ones to calculate the ratio
\(2lw + 2wh+2lh = 2 (2 \times 2 ) + 2 (2 \times 4 ) + 2 (2 \times 4 ) = 40\) square inches per smal rectangular solid.
\(40 \times 864 = 34,560\) square inches
the ratio is \(\frac{34,560}{3,456} = \frac{10}{1}\)
E is the answer.
PS: again, this is NOT a question you will ever meet during the real GRE
