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

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A cube and a pyramid of square base share the same dimensions: length,  [#permalink]

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New post 04 Sep 2016, 04:31
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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

Attachment:
T6255.png
T6255.png [ 5.8 KiB | Viewed 1528 times ]

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Re: A cube and a pyramid of square base share the same dimensions: length,  [#permalink]

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New post 04 Sep 2016, 05:22
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]

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New post 05 Dec 2018, 08:37
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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Re: A cube and a pyramid of square base share the same dimensions: length,  [#permalink]

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New post 23 Jan 2019, 05:37
Bunuel wrote:
Image
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

Attachment:
T6255.png


What is the formula for surface area of pyramid?
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Re: A cube and a pyramid of square base share the same dimensions: length,  [#permalink]

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New post 23 Jan 2019, 06:10
1
emma4490 wrote:
Bunuel wrote:
Image
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

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] 23 Jan 2019, 06:10
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A cube and a pyramid of square base share the same dimensions: length,

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