Question

A cuboid of dimension 60cm ×54cm×30cm. How many small cubes with 6cm can be placed in the given cuboid?

Answer 1

Hint: We will use the formula of cuboid to solve this question. The volume of cuboid whose length is l, breadth is b and height is h is given by, V=lbh. And the volume of the cube is given by V’= side cube.

Complete step-by-step answer:

So, we have the length of the cuboid as l = 60cm, the breadth of the cuboid as b = 54cm and the height of the cuboid is h = 30 cm.
Substituting the values of length, breadth and height as above we get,
Volume of cuboid = V = lbh
\[V=lbh=60cm\text{ }\!\!\times\!\!\text{ }54cm\text{ }\!\!\times\!\!\text{ }30cm=97200c{{m}^{3}}\]
Therefore, we get the Volume of the cuboid is \[97200c{{m}^{3}}\].
Now given that the side of cube = 6 cm
Applying the volume of the cube we get,
Volume of cube = side cube.
The volume of the cube is \[{{6}^{3}}\].
So, we obtain the volume of the cube of side 6cm is V’ = \[216c{{m}^{3}}\].
Now the number of cubes can be placed in a given cuboid = \[\dfrac{\text{volume of cuboid}}{\text{volume of cube}}\].
Substituting both the values we get,
The number of cubes can be placed in a given cuboid = \[\dfrac{97200}{216}\]
Therefore, the number of cubes can be placed in a given cuboid = 450
Hence 450 cubes can be placed in the given cuboid.

Note: The possibility of error in this question can be at the point where we use the formula of calculating number of cubes. The formula is obtained by dividing the volume of cuboid by the volume of one cube, and not by volume of total cubes.