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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, 12:42
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Difficulty:

85% (hard)

Question Stats:

52% (02:24) correct 48% (01:56) wrong based on 61 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: 52161
Re: A right circular cylinder of height 1 meter and radius 9√2 centimeters  [#permalink]

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25 May 2017, 13:31
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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.

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Joined: 24 Jun 2018
Posts: 7
A right circular cylinder of height 1 meter and radius 9√2 centimeters  [#permalink]

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23 Dec 2018, 14:15
Attachment:

drawisland.png [ 23.45 KiB | Viewed 191 times ]

If the cylinder is observed from top, the diagram of the base can be drawn as above.

Since, the cubes are to be arranged in such a way that they appear as a square from top, we can visualise a square with side a as shown above.

Now as we can see that the radius of the circle may also be drawn to coincide with the diagonal of the square, we can write \sqrt{2}a = r

We know r =9\sqrt{2}

Hence we get a=18 ie. the side of square is 18.

Since the side of a cube is equal to 3 cm, 18/3 = 6 ie. 6 cubes may fit along one length of the square.

6 x 6 = 36 ie. 36 cubes may fit inside the square inscribed in the circular area of our cylinder.

Since the height of the cylinder is 100cm, 100/3 = 33.3 ~ 33. Hence we get 33 complete layers.

We already know that 36 cubes fit one layer.

Hence 36 x 33 = 1188
A right circular cylinder of height 1 meter and radius 9√2 centimeters &nbs [#permalink] 23 Dec 2018, 14:15
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