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A right circular cylinder of height 1 meter and radius 9√2 centimeters

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Joined: 14 Sep 2015
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Location: India
GMAT 1: 700 Q45 V40
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A right circular cylinder of height 1 meter and radius 9√2 centimeters  [#permalink]

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New post 25 May 2017, 13:42
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A right circular cylinder of height 1 meter and radius \(9\sqrt{2}\) centimeters is to be used to store cubes of side length 3 cm each. If in each layer of cubes stored in the cylinder, the cubes are arranged such that the top view of the layer is a square, what is the maximum number of cubes that can be stored in the cylinder? (1 meter = 100 centimeters)


A. 198
B. 200
C. 600
D. 1188
E. 1200
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Posts: 49300
Re: A right circular cylinder of height 1 meter and radius 9√2 centimeters  [#permalink]

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New post 25 May 2017, 14:31
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niteshwaghray wrote:
A right circular cylinder of height 1 meter and radius \(9\sqrt{2}\) centimetres is to be used to store cubes of side length 3 cm each. If in each layer of cubes stored in the cylinder, the cubes are arranged such that the top view of the layer is a square, what is the maximum number of cubes that can be stored in the cylinder? (1 meter = 100 centimeters)


A. 198
B. 200
C. 600
D. 1188
E. 1200


In each layer of cubes stored in the cylinder, the cubes are arranged such that the top view of the layer is a square means that little cubes make a larger square. The largest square, therefore would be an inscribed square in the circle. Largest inscribed square in the circle of radius \(9\sqrt{2}\), will have the diagonal of twice of that (the diagonal of the inscribed square = the diameter of circle). So, the diagonal of the inscribed square would be \(18\sqrt{2}\). This gives the side of the square equal to 18.

A square 18 by 18, can fit the bases of 6*6 = 36 cubes.

The height of 1 meters = 100 centimetres, can fit 33 cubes.

Total = 33*36 = 1188 cubes.

Answer: D.
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Re: A right circular cylinder of height 1 meter and radius 9√2 centimeters &nbs [#permalink] 25 May 2017, 14:31
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