Question

the breadth of a room is half of its length .its height is 3 metre and area of walls is 108m². find the volume of room.​

Answer 1

Given :-

• The breadth of a room is half of its length and its height is 3 metre.
• Area of walls is 108m².

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To Find :-

• The volume of room.

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Used Formulaes :-

♣️ Surface area of Cuboid formula :

★ $\pink{ \boxed{ \bf \pink{Surface \: area \: _{(Cuboid)} \: = \: 2(l+b) \: h}}} \:$ ★

♣️ Volume of Cubiod formula :

★ $\pink{ \boxed{ \bf Volume \: _{(Cuboid)} \: = \: l \times b \times h}}$ ★

Where,

• L = Length
• B = Breadth
• H = Height

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Solution :-

First, We have to find the breadth and length of the room :

Let,

$\bf⟼ \: Breadth \: _{(room)} \: = \: x \: m$

$\bf⟼ \: Length \: _{(room)} \: = \: 2x \: m$

Given :

• Breadth = x
• Length = 2x
• Height = 3 m
• Area = 108 m²

According to the question by using formula we get,

$\bf \implies \: Surface \: area \: _{(Cuboid)} \: = \: 2(l+b) \: h$

$\sf \implies \: 108m^{2} \: = \: 2(2x+x) \: 3$

$\sf \implies \: 108m^{2} \: = (4x + 2x)\: 3$

$\sf \implies \: 108m^{2} \: = (6x)\: 3$

$\sf \implies \: 108m^{2} \: = 18x$

$\displaystyle\sf \implies \: \cancel\frac{108}{18} \: = x$

$\displaystyle\sf \implies \: \frac{6}{1} \: = x$

$\displaystyle\sf \implies \: 6 \: = x$

$\bf \red{ \implies \: x = 6}$

Hence, the required breadth and length of a room is :

$\bf ⇢ \: Breadth \: _{(room)} \: = \: x \: m$

$\bf⇢ \: \red{ Breadth \: _{(room)} \: = \: 6\: m }$

And,

$\bf ⇢ \: Length \: _{(room)} \: = \: 2x \: m$

$\bf ⇢ \: Length \: _{(room)} \: = \: 2(6)\: m$

$\bf ⇢ \red{\: Length \: _{(room)} \: = \: 12\: m }$

∴ The breadth and length of the room is 6 meters and 12 meters .

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Now, We have to find the volume of the room :

Given :

• Length = 12 m
• Breadth = 6 m
• Height = 3 m

According to the question by using formula we get,

$\bf \implies \: Volume \: _{(room)} \: = \: l \times b \times h$

$\bf \implies\: Volume \: _{(room)} \: = \: 12 \: m\times 6 \: m \times 3 \: m$

$\bf \red{ \implies \: Volume \: _{(room)} \: = \: 216 \: {m}^{3} }$

∴ The volume of the room is 216 m³ .

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