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14 Oct 2021, 02:45
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E
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
45%
(medium)
Question Stats:
58% (01:42) correct
42%
(01:38)
wrong
based on 31
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Not Attempted Yet
The figure above shows a solid cube 3 inches on a side but with a 1-inch square hole cut through it. How many square inches is the total surface area of the resulting solid figure?
(A) 24
(B) 42
(C) 52
(D) 58
(E) 64
Attachment:
1.jpg [ 14.41 KiB | Viewed 2055 times ]
AmandeepSingh0796
14 Oct 2021, 04:07
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The area of the resulting figure will be following
T.S.A of Square - Area of 2 square cutouts + Area of 4 rectangles now inside the square
3*3*6 - 2*1*1 + 4*3*1
54-2+12
64
T.S.A of Square - Area of 2 square cutouts + Area of 4 rectangles now inside the square
3*3*6 - 2*1*1 + 4*3*1
54-2+12
64
09 Dec 2021, 08:43
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Bunuel
AmandeepSingh0796 has already done a fabulous job, just adding the figure for a bit more clarity.
Please refer to the picture below:
Attachment:
Cube .png [ 48.62 KiB | Viewed 1620 times ]
Imagine a white colored cube is completely immersed in a bucket of green paint, and then removed.
The whole outer surface of the cube would then be painted Green.
Now if we remove a portion of the cube as described in the question, the removed portion would look like the portion as shown in fig. \(2\) above.
Initially before operation " cutting a rectangle out " the total surface area of the cube is :
\(6* s^2 \) where \(s\) is a side of a cube , hence \(6* (3)^2 = 54\)
Now when we remove a rectange as shown in the fig above , the remaining cube has a surface area:
\(9+9+9+9+(9-1)+(9-1) -\) > four surfaces remain intact , from other \(2\) surfaces we remove \(1\) sq. inch
\(= 52 \)
Additionally we are left with extra four rectangles that are part of the original cube,each of area \(3*1\), these are shown as unpainted in the second fig. hence \(4*3*1= 12 \)
So now total surface area of the original cube after the operation = \(52 +12 =64\)
Total surface area actually increases since after the removal, we have \(4\) extra rectangles that form inside of the original cube.
Ans E
Hope it's clear.
