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# M24-17

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Math Expert
Joined: 02 Sep 2009
Posts: 51258

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16 Sep 2014, 00:21
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Difficulty:

55% (hard)

Question Stats:

63% (00:45) correct 37% (01:38) wrong based on 130 sessions

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A diameter of a figure is defined as a maximum distance AB where points A, B belong to the figure. For example, the diameter of the parallelogram is the parallelogram's longer diagonal. If the diameter of the cube is 3, what is the area of the surface of the cube?

A. 3
B. 6
C. $$6\sqrt{3}$$
D. 18
E. $$12\sqrt{3}$$

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Joined: 02 Sep 2009
Posts: 51258

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16 Sep 2014, 00:21
1
1
Official Solution:

A diameter of a figure is defined as a maximum distance AB where points A, B belong to the figure. For example, the diameter of the parallelogram is the parallelogram's longer diagonal. If the diameter of the cube is 3, what is the area of the surface of the cube?

A. 3
B. 6
C. $$6\sqrt{3}$$
D. 18
E. $$12\sqrt{3}$$

If $$x$$ is the length of the edge of the cube, the diameter of the cube is $$\sqrt{x^2 + x^2 + x^2} = 3$$. From this equation, $$x = \sqrt{3}$$. The area of the surface $$= 6(\sqrt{3})^2 = 18$$.

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16 Dec 2014, 22:50
Bunuel wrote:
Official Solution:

A diameter of a figure is defined as a maximum distance AB where points A, B belong to the figure. For example, the diameter of the parallelogram is the parallelogram's longer diagonal. If the diameter of the cube is 3, what is the area of the surface of the cube?

A. 3
B. 6
C. $$6\sqrt{3}$$
D. 18
E. $$12\sqrt{3}$$

If $$x$$ is the length of the edge of the cube, the diameter of the cube is $$\sqrt{x^2 + x^2 + x^2} = 3$$. From this equation, $$x = \sqrt{3}$$. The area of the surface $$= 6(\sqrt{3})^2 = 18$$.

Hi,

i am unable to understand this step.

diameter of the cube is \sqrt{x^2 + x^2 + x^2} = 3

would you please elaborate. Thank you
Director
Joined: 25 Apr 2012
Posts: 684
Location: India
GPA: 3.21

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16 Dec 2014, 23:41
1
arunpkumar wrote:
Bunuel wrote:
Official Solution:

A diameter of a figure is defined as a maximum distance AB where points A, B belong to the figure. For example, the diameter of the parallelogram is the parallelogram's longer diagonal. If the diameter of the cube is 3, what is the area of the surface of the cube?

A. 3
B. 6
C. $$6\sqrt{3}$$
D. 18
E. $$12\sqrt{3}$$

If $$x$$ is the length of the edge of the cube, the diameter of the cube is $$\sqrt{x^2 + x^2 + x^2} = 3$$. From this equation, $$x = \sqrt{3}$$. The area of the surface $$= 6(\sqrt{3})^2 = 18$$.

Hi,

i am unable to understand this step.

diameter of the cube is \sqrt{x^2 + x^2 + x^2} = 3

would you please elaborate. Thank you

The longest length in a cube of $$\sqrt{sum of square of 3 sides}$$, which will be equal to the length of longer diagonal of parallelogram ie 3
refer to the figure..
Attachment:
Untitled.jpg

To find the length of the BlackLine, you need to know the length Red line and yellow line

Length of red line: $$\sqrt{x^2+x^2}=\sqrt{2x}=b$$

length of Yellow line =x

So length of Black line =$$\sqrt{(b)^2+x^2}=\sqrt{3x}= 3$$

This can be
Refer to the chapter of 3D geometries to get a better idea math-3-d-geometries-102044.html#p792331
>> !!!

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Intern
Joined: 20 Jan 2013
Posts: 9
GMAT 1: 660 Q49 V30

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06 Sep 2016, 04:19
Your question states "If the diameter of the cube is 3, what is the area of the surface of the cube?" Answer should be A

Area of surface = \sqrt{3^2} Total surface area = 6 \sqrt{3^2}
Math Expert
Joined: 02 Sep 2009
Posts: 51258

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06 Sep 2016, 04:24
am265531 wrote:
Your question states "If the diameter of the cube is 3, what is the area of the surface of the cube?" Answer should be A

Area of surface = \sqrt{3^2} Total surface area = 6 \sqrt{3^2}

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GMAT 2: 700 Q48 V38
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30 Apr 2018, 02:24
+1 for option D. The diagonal of a cube is a*(sqrt3). a=sqrt(3). Surface area of the cube is 6*a*a. The surface area is 6*3 or 18.

Hence option D it is ...
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Senior Manager
Joined: 15 Nov 2016
Posts: 282

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19 Aug 2018, 21:53
Bunuel wrote:
Official Solution:

A diameter of a figure is defined as a maximum distance AB where points A, B belong to the figure. For example, the diameter of the parallelogram is the parallelogram's longer diagonal. If the diameter of the cube is 3, what is the area of the surface of the cube?

A. 3
B. 6
C. $$6\sqrt{3}$$
D. 18
E. $$12\sqrt{3}$$

If $$x$$ is the length of the edge of the cube, the diameter of the cube is $$\sqrt{x^2 + x^2 + x^2} = 3$$. From this equation, $$x = \sqrt{3}$$. The area of the surface $$= 6(\sqrt{3})^2 = 18$$.

Hi Bunuel,

request you to explain why $$\sqrt{x^2 + x^2 + x^2} = 3$$ ... I do not follow this...
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Math Expert
Joined: 02 Sep 2009
Posts: 51258

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19 Aug 2018, 22:47
1
ENEM wrote:
Bunuel wrote:
Official Solution:

A diameter of a figure is defined as a maximum distance AB where points A, B belong to the figure. For example, the diameter of the parallelogram is the parallelogram's longer diagonal. If the diameter of the cube is 3, what is the area of the surface of the cube?

A. 3
B. 6
C. $$6\sqrt{3}$$
D. 18
E. $$12\sqrt{3}$$

If $$x$$ is the length of the edge of the cube, the diameter of the cube is $$\sqrt{x^2 + x^2 + x^2} = 3$$. From this equation, $$x = \sqrt{3}$$. The area of the surface $$= 6(\sqrt{3})^2 = 18$$.

Hi Bunuel,

request you to explain why $$\sqrt{x^2 + x^2 + x^2} = 3$$ ... I do not follow this...

Check below:

a^2 + a^2 = d^2 (where d is the length of the diagonal of the base)
d^2 + a^2 = D^2 (where D is the longer diagoanal). Substitute d^2 to get (a^2 + a^2) + a^2 = D^2 --> $$\sqrt{a^2 + a^2 + a^2} = D$$.

Attachment:
main-qimg-e4e631d93f476069c499529cdc215a32.png

>> !!!

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Joined: 02 Feb 2018
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09 Nov 2018, 08:11

My understanding:
-diameter of cube = 3D diagonal of cube
-3D diagonal of cube = a * $$\sqrt{3}$$
-"diameter of the cube is 3" (prompt) -> 3 = a * $$\sqrt{3}$$ -> a = $$\frac{3}{\sqrt{3}}$$ and not $$\sqrt{3}$$
-area of surface: 6 * $$a^2$$ = 6 * $$(\frac{3}{\sqrt{3}})^2$$ = 18

so I get the same end result but a different value for the side of cube a
Re: M24-17 &nbs [#permalink] 09 Nov 2018, 08:11
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# M24-17

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