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If the solid above is half of a cube, then volume of the solid is

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Math Expert
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Joined: 02 Sep 2009
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If the solid above is half of a cube, then volume of the solid is  [#permalink]

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New post 08 Jan 2019, 05:11
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A
B
C
D
E

Difficulty:

  55% (hard)

Question Stats:

49% (01:31) correct 51% (01:03) wrong based on 46 sessions

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Joined: 18 Aug 2017
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Location: India
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Re: If the solid above is half of a cube, then volume of the solid is  [#permalink]

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New post 08 Jan 2019, 05:21
Bunuel wrote:
Image
If the solid above is half of a cube, then volume of the solid is

A. 16
B. 32
C. 42
D. 64
E. \(64\sqrt{2}\)


Attachment:
2019-01-08_1609.png


from given fig we can determine that the side of cube would be 4

vol of complete cube = 64
since the sold is half of cube so its vol = 32.. IMO B
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Re: If the solid above is half of a cube, then volume of the solid is  [#permalink]

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New post 08 Jan 2019, 07:49
Bunuel wrote:
Image
If the solid above is half of a cube, then volume of the solid is

A. 16
B. 32
C. 42
D. 64
E. \(64\sqrt{2}\)


Attachment:
2019-01-08_1609.png


How can a half cube look like the given figure? When it is cut across the diagonals of two parallel faces, you get this kind of a figure. The length of the diagonal of the cube is \(4*\sqrt{2}\). So the length of the side is 4 (since the sides of a 45-45-90 triangle are in the ratio \(1:1:\sqrt{2}\))

Volume of cube = 4^3 = 64

Volume of half cube (solid shown in the figure) is 32

Answer (B)
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Re: If the solid above is half of a cube, then volume of the solid is  [#permalink]

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New post 08 Jan 2019, 21:06
Bunuel wrote:
Image
If the solid above is half of a cube, then volume of the solid is

A. 16
B. 32
C. 42
D. 64
E. \(64\sqrt{2}\)


Attachment:
2019-01-08_1609.png


Bunnel, could you please provide answer
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Re: If the solid above is half of a cube, then volume of the solid is   [#permalink] 08 Jan 2019, 21:06
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