Ex.11.4 Q4 Mensuration Solution - NCERT Maths Class 8

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Question

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
Mensuration
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.

Steps:

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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