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M24-17

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Bunuel
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M24-17 [#permalink] 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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D
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Bunuel
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Re M24-17 [#permalink] New post   16 Sep 2014, 01:21
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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] 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] New post   17 Dec 2014, 00:41
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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
Untitled.jpg [ 42.81 KiB | Viewed 15254 times ]

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] 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] New post   06 Sep 2016, 05:24
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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] 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] 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] New post   19 Aug 2018, 23:47
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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:


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 --> \(\sqrt{a^2 + a^2 + a^2} = D\).

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main-qimg-e4e631d93f476069c499529cdc215a32.png [ 3.19 KiB | Viewed 9164 times ]
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Re: M24-17 [#permalink] New post   09 Nov 2018, 09:11
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Bunuel please help, I can't find my mistake...

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
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Re: M24-17 [#permalink] New post   05 Oct 2019, 22:16
I guessed correctly, but my fatal error was assuming a cube automatically gave special rights - 30-60-90 as well as 45-45-90.
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Re: M24-17 [#permalink] New post   29 Aug 2021, 03:55
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According to the question diagonal is defined as the longest diagonal of a figure.
Incase of cube if each side is equal to x then the longest diagonal will be the body diagonal whose value is given as 3
=\(\sqrt{x²+x²+x²}\)
\(\sqrt{3x²}\)=3
x=\(\sqrt{3}\)

Hence total surface area of cube is 6x²=6*\(\sqrt{3}\)²
=6*3=18

Hence IMO d is the correct option.
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Re: M24-17 [#permalink]
29 Aug 2021, 03:55
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