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There are spheres each of radius 1 cm. The maximum number of

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by Anurag@Gurome » Tue Jul 10, 2012 5:49 am
gmatter2012 wrote:There are spheres each of radius 1 cm. The maximum number of spheres that can be put in a cubical box of side 5 cm is?
The maximum dimension of the sphere is the diameter of the sphere = 2 cm
Now, the maximum number of spheres that we can put side by side must be equal to the greatest integer less than or equal to 5/2 = 2.5

Hence, we can put maximum 2 spheres side by side.
Now, try to visualize the situation. Each side of the cube is occupied by two spheres. Hence, there are two layers of spheres inside the cube one above another. And each layers contains 4 spheres each.

Hence, total number of spheres = 2*4 = 8

The correct answer is B.

Note : If you visualize the situation you will see that if we push the 8 spheres as much as we can towards the 8 corners of the cube, we will have some amount of space at the center of the cube. And that place may hold one more sphere. If 9 was in the option, we had to calculate whether that empty space is enough to hold one more sphere. As 9 is not in the option, we are not doing that calculation.
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by gmatter2012 » Tue Jul 10, 2012 5:59 am
Anurag@Gurome wrote:
gmatter2012 wrote:There are spheres each of radius 1 cm. The maximum number of spheres that can be put in a cubical box of side 5 cm is?
The maximum dimension of the sphere is the diameter of the sphere = 2 cm
Now, the maximum number of spheres that we can put side by side must be equal to the greatest integer less than or equal to 5/2 = 2.5

Hence, we can put maximum 2 spheres side by side.
Now, try to visualize the situation. Each side of the cube is occupied by two spheres. Hence, there are two layers of spheres inside the cube one above another. And each layers contains 4 spheres each.

Hence, total number of spheres = 2*4 = 8

The correct answer is B.

Note : If you visualize the situation you will see that if we push the 8 spheres as much as we can towards the 8 corners of the cube, we will have some amount of space at the center of the cube. And that place may hold one more sphere. If 9 was in the option, we had to calculate whether that empty space is enough to hold one more sphere. As 9 is not in the option, we are not doing that calculation.
Awesome !
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