Question of the week - 46(A pastry is in the shape of a cube, .....)

Question

e-GMAT          Question of the Week - 46

A hollow box is in the shape of a cube, that has a side length of 2 metres. If a portion of it is cut along three adjacent face diagonals of the cube, then what is the total surface area of remaining larger piece of the box?

A.  4
 B.  6
 C.  16
 D.  18
 E.  24

https://e-gmat.com/blogs/wp-content/uploads/2018/08/Quant-workshop_Webinar-e1533628475738.jpg

Archit3110 · Answer

giving a try
visualize that the cut of the cake along three sides is done on one of the faces along the digaonal

TSA; 6*s^2 ; 24 
and digaonal ; 2√2
along the diagonal cake is cut gives us three ∆ ; area;; 1/2 * 2*2 ; 2 *3 ; 6
left area l 24-6 = 18
IMO D

nick1816 · Answer

We will get smaller piece, a tetrahedron having 3 faces as right angle isosceles triangles whose equal sides are 2 cm, and fourth face is equilateral triangle having side  2\sqrt{2} .
We can't find the area of a 3-D figure. It should be either volume, curved surface area or total surface area.

RupamPaul13 · Answer

Posted from my mobile device

Kinshook · Answer

Total surface area of original cube = 6 * 4 = 24 sq m
Cut area = 3 * 1/2 *(2*2) = 6 sq m 
Since there are 3 right angled triangles of base 2 & height 2 m cut from the original cube
Thus remaining area = 24 - 6 = 18 sq m

Alternatively remaining area = 3 * (2*2) + 3 * 1/2 (2*2) = 18 sq m 
since there are 3 sides 0f 2*2 sq m = 12 sq m 
and there are 3 right angles triangles of are = 3 * 1/2 (2*2) = 6 sq m

The solutions do not include area of equilateral triangle generated as a result of the cut = 2 \sqrt{3} .

RupamPaul13 · Answer

Posted from my mobile device

EgmatQuantExpert · Answer

Hi @nikh1816,

When we say area, it implicitly means TSA. Anyway, we have edited the question to remove all the ambiguity.

Thanks & Regards,

Archit3110 · Answer

EgmatQuantExpert ; thanks for editing the question .. else considering volume as answer would have been 6 ... nick1816

nick1816 · Answer

Thanks for editing. But if we're considering TSA, then we should not exclude the area of the equilateral triangle that's left after we removed the cutting portion. None of the options is correct in that scenario. That's why i was confused. Imo question is poorly written and designed.

EgmatQuantExpert · Answer

Hi  nick1816 ,

Thanks for pointing out the issue.

Apologies, we have edited the question now.

Thanks & Regards,

Vinit800HBS · Answer

The question is still incorrect  EgmatQuantExpert

Because the box is hollow, on cutting it along the given dimensions, the inside portion will get exposed and thus will increase the area. In fact, whatever is the surface area of the outside portion, the same area would be inside after cutting the hollow box.

Still, the question is wrong. Please check

Posted from my mobile device

aliakberza · Answer

Hi  Archit3110 . Thanks for the solution. Could you please explain to me why it would be 3 triangles and not 4? what about the base of the shape is that not the 4th side. I followed the same method but when I tried to visualize the shape, to me the it seemed that the shape would have four faces. What am I missing?

Thanks in advance!

EgmatQuantExpert · Answer

Solution 
  Given:  
 • A hollow box is in the shape of a cube that has a side length of 2 meters
• A portion of it is cut along three adjacent face diagonals of the cube

To find:  
 • The total surface area of remaining larger piece of the box

Approach and Working out:   
 • A hollow box has all sides closed, and the total surface = 6 * area of a face.

Now, let us try to visualize the hollow box after it is cut along three adjacent face diagonals of the cube.

https://e-gmat.com/blogs/wp-content/uploads/2019/07/Qow-46-P1.png   https://e-gmat.com/blogs/wp-content/uploads/2019/07/Qow-46-P2.png   https://e-gmat.com/blogs/wp-content/uploads/2019/07/Qow-46-P3.png 
 
 • From the third figure, we can see that the total surface area of the larger piece =  3 * area of a face + 3 * \frac{area of a face}{2}

Note:   we should not consider the area of the triangle in total surface area, since the box is hollow.
 • Area of a face =  (side length)^2 = 2^2 = 4  
 • Therefore, the total surface area of the larger piece =  3 * 4 + 3 * \frac{4}{2} = 12 + 6 = 18  sq. meters

Hence, the correct answer is Option D.

Answer: D

https://e-gmat.com/blogs/wp-content/uploads/2018/07/FT-GC-FB-event-e1532524398949.jpg

DarkHorse2019 · Answer

This problem is so easy yet so difficult. errr. Let me re-phrase my sentence

This problem is so difficult if you cannot visualize the diagram, and so easy when you are able to visualize (or draw) it correctly. Thank you so much for the diagram EgmatQuantExpert

bumpbot · Answer

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Question of the week - 46(A pastry is in the shape of a cube, .....)

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Question of the week - 46(A pastry is in the shape of a cube, .....)

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