Question

A cuboid is of dimensions 60 cm × 54 cm × 30 cm. How many small cubes with side 6 cm can be placed in the given cuboid​

Answer 1

Answer:

Volume of cuboid = lbh = 60×54×30

= 97200cm³

Volume of cube = l³

Here, l= 6 cm

So,

Volume of cube = 6³= 216cm³

No of cubes placed in given cuboid = Volume of cuboid

Volume of cube

= 97200/216

= 450 cubes

So, 450 cubes can be placed in a given cuboid.

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Answer 2

$\large\underline{\sf{\pmb{Given}}}$

➠ A cuboid is of dimensions 60 cm x 54 cm x 30 cm.

$\begin{gathered} \: \: \end{gathered}$

$\large\underline{\sf {\pmb{To \: Find}}}$

➠ How many small cubes with side 6 cm can be placed in the given cuboid?

$\begin{gathered} \: \: \end{gathered}$

$\large\underline{\sf{ \pmb{Using \: Formula }}}$

$\bigstar \: \underline{ \boxed{\sf {Volume \: of \: a \: cuboid = (Length \times Breadth \times Height) }}}★$

$\bigstar \: \underline { \boxed{\sf{{Volume \: of \: a \: cube = ( {a}^{3} ) }}}}★$

$\bigstar \: \underline{ \boxed{\sf{{Required \: number \: of \: Cube = \dfrac{Volume \: of \: Cuboid}{volume \: of \: the \: small \: cube} }}}}★$

Where

$\leadsto \sf{a = Side }⇝a=Side$

$\begin{gathered} \: \: \end{gathered}$

$\large\underline{\sf{ \pmb{Solution}}}$

Firstly finding the volume of a cuboid

${ \implies\sf{Volume \: of \: a \: cuboid = (Length \times Breadth \times Height) }}$

Substituting the values

${\implies \sf{ Volume_{(cuboid) }= (60 cm \times 54 cm \times 30 cm) }}$

${\implies \sf { Volume_{(cuboid) }= 97200 \: {cm}^{3} }}$

$\: \: \: \star \: \underline {\boxed{\sf \purple{{volume \: of \: a \: cuboid = 97200 \: {cm}^{3} }}}} \: \star⋆$

⋆

$\begin{gathered} \: \: \end{gathered}$

Now Finding the volume of a cube

$\implies{\sf{{Volume \: of \: a \: cube = ( {a}^{3} ) }}}$

Substituting the values

${ \implies \sf{Volume_{(cube)} = (6 cm \times 6 cm \times 6 cm) }}$

${ \implies \sf{Volume_{(cube)} = 216 \: {cm}^{3} }}$

$\: \: \: \star \: \underline {\boxed{\sf \purple{{Volume \: of \: a \: cube = 216 \: {cm}^{3} }}}} \: \star⋆$

⋆

$\begin{gathered} \: \: \end{gathered}$

Finding the number of cubes placed in the cuboid

${\implies\sf{{Required \: number \: of \: Cube = \dfrac{Volume \: of \: Cuboid}{volume \: of \: the \: small \: cube} }}}$

Substituting the values

$\implies \sf Number \: of \: cubes = \dfrac{97200}{216}$

$\implies \sf Number \: of \: cubes = \cancel\dfrac{97200}{216}$

$\implies\sf{Number \: of \: cubes = 450}$

$\: \: \: \large \star \: \underline {\boxed{\sf \purple{Number \: of \: cubes = {450}}}} \: \star⋆$

⋆

$\begin{gathered} \: \: \end{gathered}$

tex]\large\underline{ \sf{\pmb{ Therefore}}} [/tex]

➠ Total 450 small cubes with side 6 cm can be placed in the given 60 cm x 54 cm x 30 cm cuboid.

$\begin{gathered} \: \: \end{gathered}$

$\large \underline{\sf{ \pmb{Additional \: Information }}}$

$\begin{gathered}\begin{gathered}\begin{gathered}\bigstar \: \bf\underline{More \: Useful \: Formulae } \: \bigstar \\ \begin{gathered}{\boxed{\begin{array} {cccc}{\sf{{\leadsto TSA \: of \: cube \: = \: 6(side)^{2}}}} \\ \\{\sf{{\leadsto LSA \: of \: cube \:= \: 4(side)^{2}}}} \\ \\{\sf{{\leadsto Volume \: of \: cube \: = \: (side)^{3}}}} \\ \\ {\sf{{\leadsto Diagonal \: of \: cube \: = \: \sqrt(l^{2} + b^{2} + h^{2}}}} \\ \\ {\sf{{\leadsto Perimeter \: of \: cube \: = \: 4(l+b+h)}}} \\ \\ {\sf{{\leadsto CSA \: of \: sphere \: = \: 2 \pi r^{2}}}} \\ \\ {\sf{{\leadsto SA \: of \: sphere \: = \: 4 \pi r^{2}}}} \\ \\{\sf{{\leadsto TSA \: of \: sphere \: = \: 3 \pi r^{2}}}} \\ \\ {\sf{{\leadsto Diameter \: of \: circle \: = \: 2r}}} \\ \\ {\sf{{\leadsto Radius \: of \: circle \: = \: \dfrac{d}{2}}}} \\ \\ {\sf{{\leadsto Volume \: of \: sphere \: = \: \dfrac{4}{3} \pi r^{3}}}} \\ \\ {\sf{{\leadsto Area \: of \: rectangle \: = \: Length \times Breadth}}} \\ \\ {\sf{{\leadsto Perimeter \: of \: rectangle \: = \:2(length+breadth)}}} \\ \\{\sf{{\leadsto Perimeter \: of \: square \: = \: 4 \times sides}}}\end{array}}}\end{gathered}\end{gathered}\end{gathered}\end{gathered}$