Inspired by the problem submitted by another user on

Question

Inspired by the problem submitted by another user on cube/cuboid, my question would be:

A rectanglar cuboid with dimensions 6 * 12 * 15 is cut into same sized cuboids of dimensions proportional to the original cuboid. What will be the least number of cuboids that can be formed ?

ssumitsh · Answer

1 just leave it as it is. :-)

However, if you have to cut, then: then you can cut it into 8 cuboids.

apandey · Answer

least number is 1. don't cut anyhing.

however 9 cuboid are possible in same proportion.

Dan · Answer

9.

with dimensions 2 * 4 * 5.

vprabhala · Answer

can you guys please explain elaborately your answer choices.

rxs0005 · Answer

Since we want to find out the least number of cubes then we should get the largest cube that can be made so highest common factor of the dimensions of 6 12 15 thats 3 so each cube will be volume 3^3 = 27 

Total cubes = 6 * 12 * 15 / 27 = 40 

Answer = 40 cubes 

rxs0005

MA · Answer

question is unclear. what is meant by proportional to the original cubiod? if it means the dimentions of the equal cubides are proportinals to the dimentions of the original cubids, then the number of cubides is 27. the dimentions of each 27 equal cubiods are 2*4*5 whcih are proportional to 6*12*15,the dimentions of the original cubids, respectively. the proportion is 3:3:3.

mein_aur_yeh_mba · Answer

Well.. the answer is 27 !

MA - the question says that the dimensions are proportional, ie the length, breadth and height of cut cuboids should be cut in such a way that its length, breadth and height are in proportion to the original cuboid respectively. It means if 6:12:15 are the sides of the original cuboid, then cut cuboid should have dimensions 6:12:15 which is 2x:4x:5x where x is a variable. 

dimension of original cuboid: 6*12*15
Volume = 1080

Cut into same proportion => 2:4:5 . This should be the sides of the cut cuboid.

Volume = 2*4*5=40

Therefore total no. of cuboids = 1080/40 = 27

Vijo · Answer

I agree with main_aur_yeh_mba.
The answer should be 27.

nocilis · Answer

I am not following this one.
The least number of cuboids will be formed if you leave the cuboid alone = 1.

mein_aur_yeh_mba · Answer

OA = 27

Note: it says "cut" . Hence it is not 1.

nocilis · Answer

If you 'have to cut', can't we cut it in to cuboids of size say 
6/Cubert(2) , 12/ Cubert(2), 15/Cubert(2) (still maintaining the ratio 6:12:15). 

The volume of such a cuboid will be 540, exactly half of the volume of original cuboid. So, least number of cuboids =2

Dan · Answer

mein_aur_yeh_mba, What 's the source of this question and its OA? 

The OA is correct up to the proportions 2*4*5, but then it uses volume to calculate the number of cuboids. 

Now, a rectanglar cuboid is a hollow or empty body, you simply cannot 'cut' the empty space and make other objects from it . You have to cut its surface area instead and form a number of cuboids from that surface area.

Unless there is another line of thinking to it that's I am missing, I just cannot agree with the OA.

Inspired by the problem submitted by another user on

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