Question

the length of a cold storage is doubled its breadth. its height is 3 metres. the area of its four walls is 180 m sq. find its volume

Answer 1

$\bold{Given : }$

The length of a cold storage is doubled its breadth. its height is 3 metres. the area of its four walls is 180 m sq.

$\bold{To \: find \: out : }$

Find the volume of cuboid?

$\bold{Formula \: used : }$

★ Area of four walls = 2 ( l + b ) × h

★ Volume of cuboid = l × b × h

$\bold{Solution }:$

Let the length, breadth and height of the cold storage be l, b and h respectively.

Then, l = 2b and h = 3m [ Given ]

Now,

$\sf{Area \: of \: the \: four \: walls = 108 {m}^{2} }$

$\rightarrow \: 2(l + b) \times h = 108$

$\rightarrow \: 2(2b + b) \times 3 = 108$

$\rightarrow \: 2 \times 3b \times 3 = 108$

$\rightarrow18b = 108$

$\rightarrow \: b = \cancel \frac{108}{18}$

$\rightarrow \: b = 6 \: m$

• Breadth = 6m

• Length = 2b = 2 × 6 = 12m

Hence,

Volume of the cold storage = length × breadth × height

= 12 × 6 × 3

= 216 m³

Answer 2

⠀⠀⠀⠀$\huge\underline{ \mathrm{ \red{QueS{\pink{tiOn}}}}}$

the length of a cold storage is doubled its breadth. its height is 3 metres. the area of its four walls is 180 m sq. find its volume

━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━

⠀⠀⠀$\huge{ \underline{ \purple{ \bold{ \underline{ \mathrm{ExPlanA{\green{TiOn }}}}}}}}$

$\rm{ \color{blue}{{Given}\begin{cases}\textsf{length = double \: to \: its \: breath}\\\textsf{height = 3m}\\\textsf{area \: of \: four \: walls = 18m \: sq} \end{cases}}}$

$\large\underline{ \underline{ \red{ \bold {To \:Find}}}}$

We need to find the volume of cuboid.

⠀⠀⠀⠀⠀$\huge\underline{ \underline{ \orange{ \bold{sOluTiOn}}}}$

⠀⠀⠀⠀⠀

$\bf\:Let$the length be x and breadth be y.

$\: \: \: \: \: \: \: \: \: \: \bf \underbrace { \color{red}{ \: according \: to \: question \: }}\\ \\ \: \: \: \: \: \bf \red{length \: is \: doubled \: to \: its \: breadth}$

⠀⠀⠀⠀⠀⠀⠀⠀so,

so,⠀⠀⠀⠀⠀⠀⠀⠀length = 2y

$\color{green} \underline{ \boxed{ \rm{area \: of \: four \: walls \: = 2 \times (l + b) \times h}}}$

➩⠀⠀⠀⠀⠀$\bf\:2\times(2y+y)\times3=108$

➩⠀⠀⠀⠀⠀$\bf\:2\times(3y)\times3=108$

➩⠀⠀⠀⠀⠀$\bf\:6\times3y=108$

➩⠀⠀⠀⠀⠀$\bf\:18y=108$

➩⠀⠀⠀⠀⠀$\bf\:y=\cancel\dfrac{108}{18}$

➩⠀⠀⠀⠀⠀$\bf\:y=6m$

⠀⠀⠀⠀⠀⠀⠀⠀⠀$\bf\:so, breadth= 6m$

➼⠀⠀⠀⠀⠀⠀⠀⠀$\bf\:length\: x=2y$

➼⠀⠀⠀⠀⠀⠀⠀⠀$\bf\:Length = 2\times6$

➨⠀⠀⠀⠀⠀$\underline{\boxed{\bf{\color{purple}{Length=12m}}}}$

${ \underline{ \boxed<strong> </strong>{\bf{ \color{blue}{volume \: of \: cold \: store \: = l \times b \times h}}}}}$

➵⠀⠀⠀⠀⠀$\bf\:= 12\times6\times3$

➤⠀⠀⠀⠀⠀$\underline{\boxed{\bf{\color{red}{volume=216{m}^{3}}}}}$

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