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

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Manager
Joined: 14 Sep 2015
Posts: 65
Location: India
GMAT 1: 700 Q45 V40
GPA: 3.41
A right circular cylinder of height 1 meter and radius 9√2 centimeters [#permalink]

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25 May 2017, 13:42
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Difficulty:

55% (hard)

Question Stats:

62% (02:48) correct 38% (02:12) wrong based on 26 sessions

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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
Math Expert
Joined: 02 Sep 2009
Posts: 46264
Re: A right circular cylinder of height 1 meter and radius 9√2 centimeters [#permalink]

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

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