question_answer 1)

                A cuboid is of dimensions \[60\,cm\times 54\,cm\times \,30\,\,cm\]. How many small cubes with side 6 cm can be placed in the given cuboid?

Answer:

                Volume of the cuboid \[=60\times 54\times 30\,c{{m}^{3}}\] \[=97200\,c{{m}^{3}}\] Volume of a small cube \[=6\times 6\times 6\,c{{m}^{3}}\]                 \[=216\,c{{m}^{3}}\] \[\therefore \] Number of small cubes that can be placed in the given cuboid \[=\frac{\text{Volume}\,\text{of}\,\text{the}\,\text{cuboid}}{\text{Volume}\,\text{of}\,\text{a}\,\text{small}\,\text{cube}}\] \[=\frac{97200}{216}\] = 450 Hence, 450 small cubes can be placed in the given cuboid.