Ex.11.4 Q4 Mensuration Solution - NCERT Maths Class 8

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A cuboid is of dimensions \(60 \rm \,cm × 54 \,cm × 30 \,cm.\) How many small cubes with side \(6 \rm\,cm\) can be placed in the given cuboid?

 Video Solution
Ex 11.4 | Question 4

Text Solution

What is Known?

Side of the cube and dimensions of the cuboid.

What is unknown?

Number of cubes that to be placed in the given cuboid.


Volume of cuboid

\[\begin{align} & = l \times b \times h \\&= 60\,{\rm{cm}} \times 54\,{\rm{cm}} \times 30\,{\rm{cm}}\\ &= 97200\,{\rm{c}}{{\rm{m}}^2}\end{align}\]

Side of the cube \(6 \rm\,cm\)

Volume of the cube 
\[\begin{align} &= (6)^3{\rm{c}}{\rm{m}}^3 = 216\,{\rm{cm}}\end{align}\]

Required number of cubes
\[\begin{align} &= \frac{{\text{volume of cuboid}}}{\text{volume of the cube}} \\ &= \frac {{97200}}{{216}}\\ &= 450\end{align}\]

Thus\(, 450\) cubes can be placed in the given cuboid.

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