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Founder  Joined: 18 Apr 2015
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The rectangular solid above is made up of eight cubes of the [#permalink]
Expert's post 00:00

Question Stats: 52% (01:05) correct 47% (01:44) wrong based on 17 sessions
Attachment: cube.jpg [ 6.26 KiB | Viewed 959 times ]

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. $$\frac{1}{3}$$
[Reveal] Spoiler: OA

_________________ Director Joined: 20 Apr 2016
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WE: Engineering (Energy and Utilities)
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Re: The rectangular solid above is made up of eight cubes of the [#permalink]
1
KUDOS
Carcass wrote:
Attachment:
The attachment cube.jpg is no longer available

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

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 = $$\frac{8}{28} = \frac{2}{7}$$
Attachments Fig 3.jpg [ 16.98 KiB | Viewed 916 times ] Fig 2.jpg [ 18.04 KiB | Viewed 914 times ] Fig 1.jpg [ 21.41 KiB | Viewed 917 times ]

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Founder  Joined: 18 Apr 2015
Posts: 7025
Followers: 117

Kudos [?]: 1372 , given: 6387

Re: The rectangular solid above is made up of eight cubes of the [#permalink]
Expert's post
Super explanation.

Regards
_________________ Re: The rectangular solid above is made up of eight cubes of the   [#permalink] 15 Jul 2018, 08:34
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