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06 Feb 2020, 05:50
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A
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Difficulty:
45%
(medium)
Question Stats:
68% (02:01) correct
32%
(02:05)
wrong
based on 132
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The dimensions of a rectangular solid are 4 inches, 5 inches, and 8 inches. If a cube, a side of which is equal to one of the dimensions of the rectangular solid, is placed entirely within the rectangular solid, what the ratio of the volume of the cube to the volume within the rectangular solid that is not occupied by the cube?
(A) 2:3
(B) 2:5
(C) 5:16
(D) 25:7
(E) 32:25
(A) 2:3
(B) 2:5
(C) 5:16
(D) 25:7
(E) 32:25
06 Feb 2020, 06:23
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For a cube to be able to be incerted it must have all sides as the smallest side of the rectangular thus 4. Otherwise it will come out of the rectangular.
then we have Square volume
4*4*4=64
Rectangular volume
4*5*8=160
160-64= 96
64:96 = 2:3
Answer A
then we have Square volume
4*4*4=64
Rectangular volume
4*5*8=160
160-64= 96
64:96 = 2:3
Answer A
06 Feb 2020, 07:32
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Bunuel
Volume of CUboid is \(4*5*8 = 160\)
Now, dimensions of the cube must be the lowest dimension of the cuboid since it won't fit in if the sides of Cube > Sides of Cuboid
So, Volume of the Cube is \(4^3 = 64\)
Now, the ratio of the volume of the cube to the volume within the rectangular solid that is not occupied by the cube is -
\(64:(160-64)\)
\(= 64 : 96\)
\(= 2 : 3\), Answer must be (A)
