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# What is the largest possible surface area you can get by removing eigh

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VP
Joined: 19 Oct 2018
Posts: 1297
Location: India
What is the largest possible surface area you can get by removing eigh  [#permalink]

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13 Nov 2019, 19:25
4
00:00

Difficulty:

65% (hard)

Question Stats:

35% (02:03) correct 65% (01:41) wrong based on 19 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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Math Expert
Joined: 02 Aug 2009
Posts: 8327
Re: What is the largest possible surface area you can get by removing eigh  [#permalink]

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13 Nov 2019, 20:58
2
nick1816 wrote:
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.

E
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Joined: 16 Feb 2015
Posts: 278
Location: United States
Concentration: Finance, Operations
Re: What is the largest possible surface area you can get by removing eigh  [#permalink]

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14 Nov 2019, 04:33
chetan2u wrote:
nick1816 wrote:
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.

E

Can you explain which eight cube should be removed, understand till 6 cubes from middles of faces.
Re: What is the largest possible surface area you can get by removing eigh   [#permalink] 14 Nov 2019, 04:33
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