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Carcass

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Joined: 18 Apr 2015

Posts: 15667

GRE 1: Q160 V160

The rectangular solid above is made up of eight cubes of the [#permalink]

13 Jul 2018, 11:54

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The rectangular solid above is made up of eight cubes of the same size, each of which has exactly one face painted blue. What is the greatest fraction of the total surface area of the solid that could be blue?

A. $\frac{1}{6}$

B. $\frac{3}{14}$

C. $\frac{1}{4}$

D. $\frac{2}{7}$

E. $\frac{1}{3}$

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pranab223

Joined: 20 Apr 2016

Posts: 1307

WE:Engineering (Energy and Utilities)

Re: The rectangular solid above is made up of eight cubes of the [#permalink]

15 Jul 2018, 07:55

Carcass wrote:

Attachment:

The attachment cube.jpg is no longer available

Here,

As per the diagram,
The total area that can be blue = 8 sides in the front + 8 sides in the back + 4 sides in the top + 4 sides in the bottom + 2 sides in left side + 2 sides in the right side = 8 + 8 + 4 + 4 + 2 + 2 = 28 sides

So since the greatest no. of sides that can be painted = 8

Therefore the greatest fraction of the total surface area of the solid that could be blue = $\frac{8}{28} = \frac{2}{7}$

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Fig 3.jpg [ 16.98 KiB | Viewed 4262 times ]

Fig 2.jpg [ 18.04 KiB | Viewed 4269 times ]

Fig 1.jpg [ 21.41 KiB | Viewed 4269 times ]

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Carcass

Verbal Expert

Joined: 18 Apr 2015

Posts: 15667

GRE 1: Q160 V160

Re: The rectangular solid above is made up of eight cubes of the [#permalink]

15 Jul 2018, 08:34

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Super explanation.

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bumpbot

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Re: The rectangular solid above is made up of eight cubes of the [#permalink]

20 Jan 2021, 06:21

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