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M24-17

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M24-17  [#permalink]

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New post 16 Sep 2014, 01:21
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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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Re M24-17  [#permalink]

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New post 16 Sep 2014, 01:21
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 \(= 6(\sqrt{3})^2 = 18\).

Answer: D
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Re: M24-17  [#permalink]

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New post 16 Dec 2014, 23:50
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 \(= 6(\sqrt{3})^2 = 18\).

Answer: D



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
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Re: M24-17  [#permalink]

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New post 17 Dec 2014, 00:41
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 \(= 6(\sqrt{3})^2 = 18\).

Answer: D



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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Re: M24-17  [#permalink]

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New post 06 Sep 2016, 05:19
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}
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Re: M24-17  [#permalink]

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New post 06 Sep 2016, 05:24
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}


That's not right. Please re-read the solution and the discussion above.
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Re: M24-17  [#permalink]

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New post 30 Apr 2018, 03:24
+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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Re: M24-17  [#permalink]

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New post 19 Aug 2018, 22:53
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 \(= 6(\sqrt{3})^2 = 18\).

Answer: D


Hi Bunuel,

request you to explain why \(\sqrt{x^2 + x^2 + x^2} = 3\) ... I do not follow this... :-o
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Re: M24-17  [#permalink]

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New post 19 Aug 2018, 23:47
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 \(= 6(\sqrt{3})^2 = 18\).

Answer: D


Hi Bunuel,

request you to explain why \(\sqrt{x^2 + x^2 + x^2} = 3\) ... I do not follow this... :-o


Check below:
Image

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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New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


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Re: M24-17 &nbs [#permalink] 19 Aug 2018, 23:47
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