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A cube and a pyramid of square base share the same dimensions: length,

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Bunuel
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A cube and a pyramid of square base share the same dimensions: length, [#permalink] New post   04 Sep 2016, 05:31
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A cube and a pyramid of square base share the same dimensions: length, width, and height. If the volume of the cube is equal to the surface area of the cube, then what is the volume of the pyramid?

A. 9
B. 64/3
C. 27
D. 72
E. 216

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tuanle
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Re: A cube and a pyramid of square base share the same dimensions: length, [#permalink] New post   04 Sep 2016, 06:22
Let a be the side of the cube.
Since the volume of the cube is equal to the surface area of the cube, a^3= 6 a^2, which implies a=6.
The volume of the pyramid is (1/3) a^3= 72.
The answer is D.
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Re: A cube and a pyramid of square base share the same dimensions length, [#permalink] New post   27 Feb 2017, 19:36
reto wrote:
A cube and a pyramid of square base share the same dimensions length, width height. If the volume of the cube is equal to the surface area of the cube, then what is the volume of the pyramid?

A. 9
B. 64/3
C. 27
D. 72
E. 216



Hi reto and all the Quant experts.

How often would we encounter geometry questions on Pyramids, Cones etc. on the GMAT ?
Asking just to ensure I dedicate optimum time towards it.

Thanks in advance. :)
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Bunuel
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Re: A cube and a pyramid of square base share the same dimensions length, [#permalink] New post   28 Feb 2017, 00:11
Expert Reply
Shruti0805 wrote:
reto wrote:
A cube and a pyramid of square base share the same dimensions length, width height. If the volume of the cube is equal to the surface area of the cube, then what is the volume of the pyramid?

A. 9
B. 64/3
C. 27
D. 72
E. 216



Hi reto and all the Quant experts.

How often would we encounter geometry questions on Pyramids, Cones etc. on the GMAT ?
Asking just to ensure I dedicate optimum time towards it.

Thanks in advance. :)


At max you'll see 1-2 questions on 3-D geometry.

Check other 3-D Geometry Questions in our Special Questions Directory.

Hope it helps.
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abhishekdadarwal2009
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Re: A cube and a pyramid of square base share the same dimensions: length, [#permalink] New post   05 Dec 2018, 09:37
given:
area of the cube=volume of the cube

this implies:
a^3=6a^2
this gives a=6

so if the side of the cube is 6 that means the area of the pyramid=1/3*a*a*a

this gives us 1/3*6*6*6=72
option D
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emma4490
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Re: A cube and a pyramid of square base share the same dimensions: length, [#permalink] New post   23 Jan 2019, 06:37
Bunuel wrote:

A cube and a pyramid of square base share the same dimensions: length, width, and height. If the volume of the cube is equal to the surface area of the cube, then what is the volume of the pyramid?

A. 9
B. 64/3
C. 27
D. 72
E. 216

Show Spoiler
Attachment:
T6255.png


What is the formula for surface area of pyramid?
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KanishkM
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Re: A cube and a pyramid of square base share the same dimensions: length, [#permalink] New post   23 Jan 2019, 07:10
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emma4490 wrote:
Bunuel wrote:

A cube and a pyramid of square base share the same dimensions: length, width, and height. If the volume of the cube is equal to the surface area of the cube, then what is the volume of the pyramid?

A. 9
B. 64/3
C. 27
D. 72
E. 216

Show Spoiler
Attachment:
T6255.png


What is the formula for surface area of pyramid?


Are you asking with respect to this question??(its quite a weird one)

But Since here we are asked to calculate the Volume of a pyramid it is => 1/3 * a^2 * h

a is side and h is the height, which will be equal here to one of the side of the square, making the formula

V = 1/3 * a^3
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Re: A cube and a pyramid of square base share the same dimensions: length, [#permalink] New post   01 Aug 2021, 06:48
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Re: A cube and a pyramid of square base share the same dimensions: length, [#permalink]
01 Aug 2021, 06:48
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