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

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The rectangular solid above is made up of eight cubes of the [#permalink]  13 Jul 2018, 11:54
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Question Stats:

63% (01:14) correct 36% (01:20) wrong based on 30 sessions
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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. $$\frac{1}{3}$$
[Reveal] Spoiler: OA

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Re: The rectangular solid above is made up of eight cubes of the [#permalink]  15 Jul 2018, 07:55
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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 = $$\frac{8}{28} = \frac{2}{7}$$
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Fig 2.jpg [ 18.04 KiB | Viewed 3156 times ]

Fig 1.jpg [ 21.41 KiB | Viewed 3155 times ]

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Re: The rectangular solid above is made up of eight cubes of the [#permalink]  15 Jul 2018, 08:34
Expert's post
Super explanation.

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

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