Question

A solid piece of metal , cuboidal in shape ,with dimension 24cm 18cm and 4cm is recast into a cube calculate lateral surface area of cube

Answer 1

${\tt{\red{\underline{\underline{\huge{Answer:=\: 576sq.cm}}}}}}$

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$\LARGE{\bf{\underline{\underline\color{blue}{GIVEN:-}}}}$

• $\sf\green{ Length\: = \: 24cm}$
• $\sf\green{ Breadth\: = \: 18cm}$
• $\sf\green{ Height\: = \: 4cm}$

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$\LARGE{\bf{\underline{\underline\color{purple}{Solution:-}}}}$

$\boxed{ \sf \red{ Volume \: of \: Cuboid }}$

$\begin{gathered}\begin{gathered}: \implies \underline{ \boxed{\displaystyle \sf \bold{\:Volume \: = \: L \: × \: B \: × \: H }} }\\ \\\end{gathered}\end{gathered}$

$\begin{gathered}\begin{gathered}: \implies \displaystyle \sf \: Volume \: = \: 24 \: × \: 18 \: × \: 4 \\ \\ \\\end{gathered}\end{gathered}$

$\begin{gathered}\begin{gathered}: \implies \underline{ \boxed{\displaystyle \sf \bold{\:Volume \: = \: 1728cm³}} }\\ \\\end{gathered}\end{gathered}$

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Volume will remains same as the same metal cuboidal is recast into cube.

$\sf\red{ Volume\: of\: cube \: =\: 1728cm³}$

$\boxed{ \sf \green{ Side\: of \: cube\: = \: cube\: root \: of \: 1728 }}$

$\fbox{12cm}$

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$\begin{gathered}\begin{gathered}: \implies \underline{ \boxed{\displaystyle \sf \bold{\:Lateral \: surface\: area \: = \: 4 \: ×\: side\: × \: side}} }\\ \\\end{gathered}\end{gathered}$

$\begin{gathered}\begin{gathered}: \implies \displaystyle \sf \: 4 \: × \: 12\: × \: 12 \\ \\ \\\end{gathered}\end{gathered}$

$\begin{gathered}\begin{gathered}: \implies \underline{ \boxed{\displaystyle \sf \bold{\:576sq.cm}} }\\ \\\end{gathered}\end{gathered}$

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