M24-17

Question

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. \(12\sqrt{3}\)

Show Answer

Official Answer

D

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

Bunuel · Answer

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. \(12\sqrt{3}\)

Show Answer

Official Answer

D

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

arunpkumar · Answer

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

WoundedTiger · Answer

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.. 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

Aditya63 · Answer

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}

Bunuel · Answer

That's not right. Please re-read the solution and the discussion above.

spetznaz · Answer

+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 ...

ENEM · Answer

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

Bunuel · Answer

Check below: https://gmatclub.com/forum/download/file.php?id=42804 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 . main-qimg-e4e631d93f476069c499529cdc215a32.png

barryseal · Answer

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

rwx5861 · Answer

I guessed correctly, but my fatal error was assuming a cube automatically gave special rights - 30-60-90 as well as 45-45-90.

Aparna05 · Answer

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.

M24-17

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