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niteshwaghray
GMAT 1: 700 Q45 V40
Posts: 59
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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
A. 198
B. 200
C. 600
D. 1188
E. 1200
niteshwaghray
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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A right circular cylinder of height 1 meter and radius 9√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
The maximum inscribed square has side = 18 cm from Pythagoras theorem. Therefore there are 6x6 = 36 cubes in each layer. 100/3 layers are possible, i.e., 33. Therefore 33x36 = 1188
shashankism
Joined: 13 Mar 2017
Last visit: 29 Jun 2026
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Posts: 612
Height = 1 meter = 100 centimeters
Radius= 9√2 centimeters
Also length of each side of a cube = 3 cm
So, First let check maximum number of cube in a layer.
Radius = 9√2 centimeters
Diagonal of he bigger square formed in top view = diameter of circle = 18√2 centimeters
Side of he bigger square formed in top view = 18 centimeters
So, No. of sqaures in a layer = 6x6 = 36
Now lets calculate the number of layer = Integral value of 100/3 = 33
So Maximum number of square that can be stored in cylinder = 36x33 = 1188
Answer D
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Radius= 9√2 centimeters
Also length of each side of a cube = 3 cm
So, First let check maximum number of cube in a layer.
Radius = 9√2 centimeters
Diagonal of he bigger square formed in top view = diameter of circle = 18√2 centimeters
Side of he bigger square formed in top view = 18 centimeters
So, No. of sqaures in a layer = 6x6 = 36
Now lets calculate the number of layer = Integral value of 100/3 = 33
So Maximum number of square that can be stored in cylinder = 36x33 = 1188
Answer D
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Attachment:
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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
Archit3110
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niteshwaghray
the radius of cylinder = 9 √2 ; the digonal of square ; 18√2 twice of the radius of the circle i.e diameter of the circle...
side of cube ; s=sV2 ; s= 18
total cubes; 18*18/3*3 = 36 cubes
given height 1mtrs = 100cm 100/3 ; 33 cubes
so 36*33; 1188
IMO D
The key is to draw a diagram so you can picture this better.
Once you do that, it's pretty easy. 33*36=1188
Once you do that, it's pretty easy. 33*36=1188
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