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The figure above shows the dimensions of a pedestal contructed of 4

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The figure above shows the dimensions of a pedestal contructed of 4  [#permalink]

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New post 10 Dec 2017, 22:23
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The figure above shows the dimensions of a pedestal contructed of 4 layers of marble. Each layer is 1 foot high and has a square base. How many cubic feet of marble make up the pedestal?

(A) 14
(B) 16
(C) 30
(D) 36
(E) 80

Attachment:
2017-12-11_1021.png
2017-12-11_1021.png [ 28.01 KiB | Viewed 427 times ]

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Re: The figure above shows the dimensions of a pedestal contructed of 4  [#permalink]

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New post 10 Dec 2017, 22:45
Image

The total marble which is used to make the pedestal is the sum of the
marble used to make the individual layers.

Formula used: Volume(cuboid) = Length*Breadth*Height

Each of the layers has a height of 1 feet.
Now, the lowest layer uses 4*4*1 or 16 cubic feet
The second lowest layer uses 3*3*1 or 9 cubic feet
The third lowest layer uses 2*2*1 or 4 cubic feet
The layer on the top uses 1*1*1 or 1 cubic feet.

Therefore, the total marble used to make the pedestal is 16+9+4+1 = 30 cubic feet(Option C)


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Re: The figure above shows the dimensions of a pedestal contructed of 4  [#permalink]

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New post 11 Dec 2017, 00:08
Bunuel wrote:
Image
The figure above shows the dimensions of a pedestal contructed of 4 layers of marble. Each layer is 1 foot high and has a square base. How many cubic feet of marble make up the pedestal?

(A) 14
(B) 16
(C) 30
(D) 36
(E) 80

Attachment:
2017-12-11_1021.png



Note that the question mentions the height of the marble layer and the figure shows the width of the top layer as 1 cm. Since the base is a square, the length will be 1 cm too.
Look at the marble layer right below it. Its width is 1 + 1 = 2 cm so its length will be 2 cm too.
The layer below it has a width of 2 + 1 = 3 cm and hence length of 3 cm too.
The layer at the bottom will have a width of 3 + 1 = 4 cm and length of 4 cm.

The total volume of marble used = Length*Width*Height = 1*1*1 + 2*2*1 + 3*3*1 + 4*4*1 = 30 cm^3

Answer (C)
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Re: The figure above shows the dimensions of a pedestal contructed of 4 &nbs [#permalink] 11 Dec 2017, 00:08
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