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

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

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

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

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

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