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25 Jun 2021, 02:15
Kudos
Bookmarks
C
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
95%
(hard)
Question Stats:
18% (02:17) correct
82%
(01:36)
wrong
based on 34
sessions
History
Date
Time
Result
Not Attempted Yet
What is the volume of the smallest cube that is needed to enclose a cuboid of dimensions 10 cm × 5 cm × 2 cm, such that the cuboid can be placed inside the cube in any possible orientation?
(A) 100 cm^3
(B) (125)^(3/2) cm^3
(C) (129)^(3/2) cm^3
(D) (100)^(3/2) cm^3
(E) (139)^(3/2) cm^3
(A) 100 cm^3
(B) (125)^(3/2) cm^3
(C) (129)^(3/2) cm^3
(D) (100)^(3/2) cm^3
(E) (139)^(3/2) cm^3
25 Jun 2021, 05:21
Kudos
Bookmarks
Bunuel
It will become much easy if we consider this cuboid to be a sphere and then adjust this sphere/ball in cube.
1) Cuboid into a sphere
The diameter of this sphere should be equal to the largest possible diagonal of the cuboid, so that the cuboid can rotate inside this sphere without any obstruction.
Largest diagonal = \(\sqrt{10^2+5^2+2^2}=\sqrt{129}\)
2) Sphere into a cube
If each side of the cube is equal to the diameter of the sphere, the sphere can roll inside the cube.
So side of cube = \(\sqrt{129}\)
Volume of the cube = \((\sqrt{129}^3\)
C
Of course the side may have to be just slightly more to ensure smooth roll of the cuboid inside, but will not effect the volume/side in any significant manner.
