Question

A cuboidal block 6cm x 9cm x 12cm is cut up into an exact number of equal cubes.The least possible number of equal cubes will be
A) 6
B) 9
C) 24
D) 30

Answer 1

A cuboidal block 6cm x 9cm x 12cm is cut up into an exact number of equal cubes.The least possible number of equal cubes will be
A) 6
B) 9
C) 24✔✔✔
D) 30

6cm x 9cm x 12cm = 648 cm³

648 cm³/3 = 24

Answer 2

Answer: There are 24 possible equal cubes.

Step-by-step explanation:

Since we have given that

Length of cuboidal block = 6 cm

Width of cuboidal block = 9 cm

Height of cuboidal block = 12 cm

So, Volume of this cuboidal block is given by

$Volume=Length\times breadth\times height\\\\=6\times 9\times 12\\\\=648\ cm^3$

Now, we need to find the least possible number of equal cubes.

So, we will find H.C.F. of 6 , 9, 12 = 3

So, Side of cube becomes 3 cm

Therefore, Volume of cubes is given by

$Side^3=3^3=27\ cm^3$

So, Least possible number of equal cubes is given by

$\frac{Volume\ of\ cuboidal\ block}{Volume\ of \ cube}\\\\=\frac{648}{27}\\\\=24$

Hence, there are 24 possible equal cubes.