Question

there is a cuboid of sides 50*40*32. feomrhis a cube is formed what is the total surface area of that cube
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Answer 1

$\LARGE\textbf{\underline{\underline{Given :-}}}$

$\large\texttt{↦ Dimensions of the cuboid = 50 × 40 × 32 }$

$\LARGE\textbf{\underline{\underline{To find :-}}}$

$\large\texttt{↦ T.S.A. of the cube formed this cuboid = ?}$

$\LARGE\textbf{\underline{\underline{Formula :-}}}$

$\large : \: \Longrightarrow\underline{\boxed{\textsf\textcolor{green}{ Volume_{ ( \: Cuboid \: ) } = L × B × H }}}\\\\\large : \: \Longrightarrow\underline{\boxed{\textsf\textcolor{green}{ Volume_ { ( \: Cube \: ) } = Side^{3} }}}\\\\\large : \: \Longrightarrow\underline{\boxed{\textsf\textcolor{green}{ T.S.A. _ { ( \: Cube \: ) } = 6 × Side^{2} }}}$

$\LARGE\textbf{\underline{\underline{How to solve :-}}}$

• As per the given Question we have to convert the cuboid into a cube , so we have to find the volume of the cuboid .

• Then we have to find the side of the cube by using the same volume of the cuboid .

• Then by using the side of the cube we have to find its T.S.A.

$\LARGE\textbf{\underline{\underline{Solution :-}}}$

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$\large:\: \bigstar\textsf\textcolor{orange}{\: \: \: Volume_{ ( \: Cuboid \: ) } = L × B × H }\\\\\\\large: \: \Longrightarrow\textsf{= 50 × 40 × 32 }\\\\\\\large: \: \Longrightarrow\textsf\textcolor{purple}{ Volume_{ ( \: Cuboid \: ) } = 64000\: unit^{3} }$

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• Now we have to assume the same volume of the cuboid to the volume of the cube to find the side of the cube .

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$\large:\: \bigstar\textsf\textcolor{orange}{\: \: \: Volume_{ ( \: Cube \: ) } = Side^{3} }\\\\\\\large: \: \Longrightarrow\textsf{64000 = Side³}\\\\\\\large: \: \Longrightarrow\textsf{ \sqrt[3]{64000} = Side }\\\\\\\large: \: \Longrightarrow\textsf{ \sqrt[3]{40 × 40 × 40 } = Side }\\\\\\\large: \: \Longrightarrow\textsf{40 = Side }\\\\\\\large : \: \therefore\underline{\boxed{\textsf\textcolor{purple}{Side of the cube = 40 units .}}}$

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$\large:\: \bigstar\textsf\textcolor{orange}{\: \: \: T.S.A. _ { ( \: Cube \: ) } = 6 × Side^{2} }\\\\\\\large: \: \Longrightarrow\textsf{= 6 × 40²}\\\\\\\large: \: \Longrightarrow\textsf{= 6 × 40 × 40}\\\\\\\large : \: \Longrightarrow\underline{\boxed{\textsf\textcolor{purple}{ T.S.A._{ ( \: Cube \: ) } = 9600 \: unit ^{2} }}}$

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