If a cube has a side of 12cm, how many cubes of side 3cm can be cut from it? what is the formula to find this?

Question

I need the formula basically, similarly for cuboid ... if two sides are mentioned....

Answer 1

Hi!
I'm guessing ur in the 9th or 10 th grade...me too!

The answer is simple-

= Volume of bigger cube
___________________
volume of smaller cube


The side of the big cube is 12cm, therefore, Volume is side x side x side = 12x12x12

Let it be in this state and dont multiply it, since 3 is a factor of 12.

Now side of smaller cube = 3cm
Therefore volume = 3x3x3

Now divide the volume of the bigger cube with the volume of the smaller cube-

12x12x12
_________
3x3x3

Now, after cancelling and simplyfiying, you get

4x4x4

which is = 64

Therefore 64 cubes of side 3cm can be made!

Similarly, for a cuboid if THREE sides are mentioned you can perform the same method as above. It is not possible to find the solution if only 2 dimensions( sides) are given...

If only two dimensions of a cuboid are given, then they should also give the volume or area of the cuboid...

Example: If a cuboid has dimensions 2cm, 4cm, 2cm how many cuboids of dimensions 1cm, 2cm, 2cm can be cut from it?

Answer: Volume of bigger cuboid
_____________________
Volume of smaller cuboid

= 2x4x2
______
1x2x2

Afer cancellation and simplifying,

Answer = 4 cuboids

There you go!

Answer 2

Calculate the volume of cube/cuboid = length x breadth x height, for both & divide...

volume of the 12cm cube = 12 x 12 x 12 = 1728 cubic cm

volume of the 3cm cube = 3 x 3 x 3 = 27 cubic cm

Number of 3cm cubes = 1728/27 = 64

Answer = 64 cubes

Answer 3

Well... you have a cube with 12cm sides and you want to divide it into 3cm cubes.

That means that there will be 4 of the little cubes along each edge, right? 4 along the bottom, 4 up the side and 4 towards the back.

If you think about it, that means that there will be 4x4x4 little cubes in the big cube. ie. 4^3 .. or 4 "cubed". Which, incidentally, is 64. Thats where the term "cubed" comes from.. x^3 is equal to the volume of a cube of side 'x'.

Answer 4

I hope this helps you :)

is the cube has a side of 12cm we need to find the volume of that cube. so 12x12x12 = 1728. which then needs to be divided by the volume of the 3cm sided cubes so if 3x3x3x = 27. we need to find what 1728 divided by 27 is. so 1728 divided by 27 is 64.
From this cube which has a side of 12cm you can make 64 cubes each with a side of 3cms.
I really hope this helped you and that i did not confuse you more. Best of luck with the school work. :)

Answer 5

Each twelve cm side has room for 4 of the 3cm sides. 4*4*4 = 64. Also you can just use the volumes. 12^3/3^3

The only hazard in using the volume is if the larger isn't an exact multiple of the smaller. While the numbers might work for say 50.5 cubes the physical reality is that you don't have partial cubes to work with.

Answer 6

You just compute the volume in cuboids.
Each cuboid is 3cm, therefore the big cube is 4 cuboids on a side, therefore the volume of the big one is 4x4x4 or 64 cuboids. Works where ever large cube is exact multiple of small ones.

Answer 7

first, calculate the volume of first cube, then calcukate the volume of the smaller cube. then devide the bigger volume by the smaller. then we will get the formula.
assume that S is the first cube's side and T is the smaller's side.

amount of cube = (SxSxS)/(TxTxT)=S^3/T^3=(S/T)^3

in this case :
amount of cube = (12/3)^3 = 4^3 = 64 cubes

Answer 8

find the volume of the larger cube by multiplying 12x12x12 to get 1728. the volume of the 3cm cube is 3x3x3=27.

since the volume of the entire cube is 1728, divide it by 27 to determine how many 3cm cubes can be obtained. the answer is 64.

im fairly sure of this answer.

Answer 9

Easy way is to calculate total volume of 12 cm cube and divide by volume of 3cm cube

Answer 10

The answer should be 12^3 / 3^3

That is the volume of the 12 cm cube divided by the volume of the 3 cm cube. Going to Windows calculator...

12^3 = 1728

3^3 = 27

1728 / 27 = 64

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