Answer

Verified

411.9k+ views

**Hint:**This question is based on the concept of volume. According to the question,

The volume of cuboid$ = n \times $ volume of small cubes, where $n$ is the number of small cubes. And we know that

Volume of cuboid$ = l \times b \times h$, where $l$ is length,$b$is breadth and $h$ is height.

Volume of cube$ = {a^3}$, where $a$ is length of any side.

**Complete step by step answer:**

In this question, we have to find the number of cubes that can be placed in the cuboid. It means that the volume of the cuboid will be equal to the sum of the volume of all small cubes that can be placed in the cuboid. Therefore,

If $n$is the number of small cubes.

Volume of cuboid$ = n \times $ volume of small cubes

$ \Rightarrow l \times b \times h = n \times {a^3}$ [Here$l$, $b$ and $h$ are the length, breadth and height of the cuboid and $a$ is the side of the cube.]

It is given that,$l = 60cm$, $b = 54cm$, $h = 30cm$ and $a = 6cm$

On substituting the values,

$\therefore 60 \times 54 \times 30 = n \times {6^3}$

$ \Rightarrow 97200 = n \times 216$

$ \Rightarrow n = \dfrac{{97200}}{{216}}$

$ \Rightarrow n = 450$

Hence there can be $450$ small cubes with side $6cm$ can be placed in the given cuboid.

**Note:**

To avoid the error one should change the unit of all the dimensions in the same unit then should start to calculate the answer.

Recently Updated Pages

What are the Advantages and Disadvantages of Algorithm

How do you write 0125 in scientific notation class 0 maths CBSE

The marks obtained by 50 students of class 10 out of class 11 maths CBSE

You are awaiting your class 10th results Meanwhile class 7 english CBSE

Which one of the following was not the cause of the class 10 social science CBSE

Which one of the following cities is not located on class 10 social science CBSE

Trending doubts

Difference Between Plant Cell and Animal Cell

Mention the different categories of ministers in the class 10 social science CBSE

Fill the blanks with the suitable prepositions 1 The class 9 english CBSE

Give 10 examples for herbs , shrubs , climbers , creepers

Who is the executive head of the Municipal Corporation class 6 social science CBSE

Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE

Which monarch called himself as the second Alexander class 10 social science CBSE

Select the word that is correctly spelled a Twelveth class 10 english CBSE

Write an application to the principal requesting five class 10 english CBSE