Question

how many cuboids of size 4 cm into 3 cm into cm can be made from a cuboid of size 12 cm into 9 cm into 6 CM

Answer 1

Let height of small cuboid be (x)cm.
No. Of Cuboids
$= \frac{Volume \: of \: big \: cube}{Volume \: of \: small \: cube} \\ = \frac{L \times B \times H}{l \times b \times h} \\ = \frac{12 \times 9 \times 6}{4 \times 3 \times x} \\ = \frac{54}{x} {cm}^{2}.$

If x is 1,
Then the answer is 54cm².

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Answer 2

first calculate all the two cubiod volume like this :-

the first cubiod volume is calculated with a volume of (length *breadth*height).
so,
the lenght is 4 cm
the breadth is 3 cm
and the height is 1 cm


insert all the values in the formula and find the volume :
$3 \times 4 \times 1$
this is when we substitute the variable with the value.

the volume of the first cubiod is 12cm^3.


the second cubiod volume is calculated by the same formulae given for the first cubiod.
so,
the length is 12 cm
the breadth is 9 cm
and the height is 6 cm

substitute all the values in the variable .

this will come like this
$12 \times 9 \times 6$

so the volume of the second cubiod is 648 cm^3.

let's compare both volume together the comparison is like this
$648 > 12$
the smallest volume will be divided by the larger volume to get the answer to your question.
$648 \div 12$
so the answer to your question is 54 small cubiod fill fit in the larger cubiod