Question

The length of a cold storage is double its breadth .its height is 3 metres the area of its four walls ( including door ) is 108 m². find its volume​

Answer 1

$\large\underline{ \underline{ \sf \maltese{ \: Question:- }}}$

• The length of a cold storage is double its breadth . Its height is 3 metres the area of its four walls ( including door ) is 108 m². Find its volume.

$\large\underline{ \underline{ \sf \maltese{ \: Given\: or \: Assume:- }}}$

• Let Length , Breadth and Height of the Cold Storage be L metres , B metres , H metres respectively.
• Length = 2b ( given )
• Height = 3 ( given )
• Area of four Walls = 108m²

$\large\underline{ \underline{ \sf \maltese{ \:To\: Find :- }}}$

• Volume of Cold Storage.

$\large\underline{ \underline{ \sf \maltese{ \: Solution:- }}}$

$\begin{gathered}\begin{gathered}\begin{gathered}: \implies \underline\blue{ \boxed{\displaystyle \sf \bold\orange{\: Area \: of \: Four \: Walls \: = \: 2( \: Length \: + \: Breadth \: ) \: \times \: Height }} }\\ \\\end{gathered}\end{gathered}\end{gathered}$

$\qquad \quad {:} \longrightarrow \sf{\sf{108 \: = \: 2( \: Length \: + \: Breadth \: ) \: \times \: Height }}$

$\qquad \quad {:} \longrightarrow \sf{\sf{108 \: = \: 2( \: 2b \: + \: Breadth \: ) \: \times \: 3 }}$

$\qquad \quad {:} \longrightarrow \sf{\sf{108 \: = \: 4b \: + \: 2b \: \times \: 3 }}$

$\qquad \quad {:} \longrightarrow \sf{\sf{108 \: = \: 18b }}$

$\qquad \quad {:} \longrightarrow \sf{\sf{ \frac{108}{18} \: = \: b }}$

$\qquad \quad {:} \longrightarrow \sf{\sf{\cancel\green{ \frac{108}{18}} \: = \: b }}$

$\qquad \quad {:} \longrightarrow \sf{\sf{ 6 \: = \: b }}$

$\qquad\quad {:} \longrightarrow \underline \red{\boxed{\sf{Breadth \: = \: 6 }}}$

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• Length = 2b = 2 × 6 = 12 metre.

$\bf \therefore \; </strong><strong>Length</strong><strong>= </strong><strong>1</strong><strong>2</strong><strong>m</strong><strong>$

$\bf \therefore \; </strong><strong>Breadth </strong><strong>= </strong><strong>6</strong><strong>m$

$\bf \therefore \; </strong><strong>Height</strong><strong> </strong><strong>= </strong><strong>3</strong><strong>m$

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$\begin{gathered}\begin{gathered}\begin{gathered}: \implies \underline\blue{ \boxed{\displaystyle \sf \bold\orange{\: Volume \: of \: Cold \: Storage\: = \: \: Length \: \times \: Breadth \: \times \: Height }} }\\ \\\end{gathered}\end{gathered}\end{gathered}$

$\quad {:} \longrightarrow \sf{\sf{ Volume \: of \: Cold \: Storage\: = \: \: 12 \: \times \: 6 \: \times \: 3}}$

$\quad {:} \longrightarrow \sf{\sf{ Volume \: of \: Cold \: Storage\: = \: 216{m}^{3}}}$

$\qquad\quad {:} \longrightarrow \underline \red{\boxed{\sf{Volume \: of \: Cold \: Storage \: = \:216{m}^{3} }}}$

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$\begin{gathered}\begin{gathered}\qquad \therefore\: \sf{ Volume \: of \: Cold \: Storage\: = \underline {\underline{ 216{m}^{3}}}}\\\end{gathered}\end{gathered}$

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Answer 2

$\begin{gathered}\begin{gathered}\qquad \therefore\: \sf{ Volume \: of \: Cold \: Storage\: = \underline {\underline{ 216{m}^{3}}}}\\\end{gathered}\end{gathered}$