Question

How many small cubes with side 6cm can be placed in the given cuboid if the cuboid has dimensions \[60cm\times 54cm\times 30cm\].

Answer 1

Hint: Find the volume of both cuboid and cube then divide them to get the number of cubes.

Given the dimensions of the cuboid are \[60cm\times 54cm\times 30cm\]
where, length= 60cm, breadth= 54cm, height= 30cm
\[\therefore \]Volume of the cuboid is given by the formula (l\times b\times h)
\[\therefore \]Volume of cuboid \[=60cm\times 54cm\times 30cm\]
Volume of cuboid \[=\left( 60\times 54\times 30 \right)c{{m}^{3}}\]
The unit of volume here is \[c{{m}^{3}}\].
Here, the side of the cube is given as 6cm.
i.e. let ‘a’ be denoted as the side of the cube.
\[\therefore a=6cm\]
The volume of a cube \[={{a}^{3}}\]
\[\therefore \]Volume of the cube \[={{6}^{3}}=6\times 6\times 6c{{m}^{3}}\]
Here, we need to find the number of cubes that can be placed inside the cuboid of dimension \[60cm\times 54cm\times 30cm\].
The required number of cubes can be found by dividing the volume of the cuboid by volume of the smaller cube.
\[\therefore \]Required number of cubes\[=\dfrac{Volume\ of\ Cuboid}{volume\ of\ cube}\]
 \[=\dfrac{\left( 60\times 54\times 30 \right)c{{m}^{3}}}{\left( 6\times 6\times 6 \right)c{{m}^{3}}}\]
Simplifying the above by cancelling out like terms, we get \[=10\times 9\times 5=450\]
\[\therefore \]450 small cubes can be placed in the given cuboid.

Note: The formula of calculating volumes of both cuboids and cubes are different. In cuboids the sides are different, whereas in cubes all sides are the same. So, the number of cubes can be found by dividing the volumes of both.