Question

010. The length of a room is double its breadth. The area of the four walls is 192 cm. If the height
of the room is 4 m, find its volume​

Answer 1

$\bf{\Huge{\underline{\boxed{\sf{\green{ANSWER\::}}}}}}$

$\bf{\large{\underline{\bf{Given\::}}}}}$

The length of a room is double its breadth. The area of the four walls is 192cm. If the height of room is 4m.

$\bf{\large{\underline{\bf{To\:find\::}}}}}$

The volume of room.

$\bf{\Large{\underline{\sf{\blue{Explanation\::}}}}}$

$\bf{We\:have\begin{cases}\sf{Let\: the\: breadth \:of \:the\: room\: be\: R.}\\ \sf{Let\: the\: length\: of\: the \:room\: be\: 2R.}\\ \sf{The \:area\:of\:four\:wall=192cm}\\ \sf{The\:height\:of\:the\:room=4m}\end{cases}}$

A/q

We know that area of the four walls: $\sf{\red{2(Length+breadth)*height}}$

→ 2(2R + R)4 = 192

→ 2(3R)4 = 192

→ 6R × 4 = 192

→ 24R = 192

→ R = $\bf{\cancel{\frac{192}{24} }}$

→ R = 8

So,

The length of the room = 2(8) = 16m.

The breadth of the room = 8m.

Now,

We know that volume of the cuboid: $\sf{\red{(Length*breadth*height)}}$

• Length of the room= 16m
• Breadth of the room= 8m
• Height of the room = 4m

→ (16 × 8 ×  4)m³

→ 512m³

Thus,

The volume of the room is 512m³.

Answer 2

Step-by-step explanation:

Let breadth of room be x cm

Then, length of room is 2x cm

According to question:

=> 4(x * 2x) = 192

=> 8x² = 192

=> x² = 24

=> x = +- 2√6

So, breadth of room is 2√6 cm

and, length is 4√6 cm

Now, volume = area of one wall * height

48 *4= 192 cm³