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705-805 (Hard)|   Geometry|      
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What is the largest possible surface area you can get by removing eigh 13 Nov 2019, 19:25
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Difficulty:

75% (hard)

Question Stats:

38% (02:05) correct 62% (02:07) wrong based on 34 sessions

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What is the largest possible surface area you can get by removing eight of the unit cubes from 27 unit cubes that are arranged in a 3×3×3 cube ?

A. 54
B. 62
C. 70
D. 74
E. 78
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E

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What is the largest possible surface area you can get by removing eigh 13 Nov 2019, 20:58
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nick1816
What is the largest possible surface area you can get by removing eight of the unit cubes from 27 unit cubes that are arranged in a 3×3×3 cube ?

A. 54
B. 62
C. 70
D. 74
E. 78
Show more


The surface area in the original cube is 6*(3*3)=6*9=54.

Now for increasing the surface area the most, remove the cubes which are least open to the air, and those will be the middle one in each face, so SIX of them
Each cube in middle has one face open, but when you remove it, there will be 5 faces open, a face on each cube adjacent to it.

A difference of 5-1= 4 units, so total 6 in middle and therefore an increase of 6*4=24 units.
Total surface area =54+24=78

Now question might be asking 6 cubes to be removed rather than 8 cubes.
If I have to still remove 2 more, I would remove 2 corner ones as each has 3 faces open and by removing them another 3 would be open, resulting in no change in surface area.

Hence answer 78

E
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What is the largest possible surface area you can get by removing eigh 14 Nov 2019, 04:33
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chetan2u
nick1816
What is the largest possible surface area you can get by removing eight of the unit cubes from 27 unit cubes that are arranged in a 3×3×3 cube ?

A. 54
B. 62
C. 70
D. 74
E. 78


The surface area in the original cube is 6*(3*3)=6*9=54.

Now for increasing the surface area the most, remove the cubes which are least open to the air, and those will be the middle one in each face, so SIX of them
Each cube in middle has one face open, but when you remove it, there will be 5 faces open, a face on each cube adjacent to it.

A difference of 5-1= 4 units, so total 6 in middle and therefore an increase of 6*4=24 units.
Total surface area =54+24=78

Now question might be asking 6 cubes to be removed rather than 8 cubes.
If I have to still remove 2 more, I would remove 2 corner ones as each has 3 faces open and by removing them another 3 would be open, resulting in no change in surface area.

Hence answer 78

E
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Can you explain which eight cube should be removed, understand till 6 cubes from middles of faces.
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What is the largest possible surface area you can get by removing eigh 15 Oct 2023, 23:23
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