Question

If a brick has length, breadth and height in the ratio 1:2:3 and the total surface area of the brick is 792 sq. m, then the volume of the brick is A) 1296m B)1396m C) 1496m D) 1596m​

Answer 1

Answer: Option (A)

Given that the dimension of a brick is in the ratio 1:2:3 i.e., Length : Breadth : Height = 1:2:3

Let the common factor of ratio of Length, breadth and height be x, then the measurements will be:

• Length = 1x
• Length = 1xBreadth = 2x
• Length = 1xBreadth = 2xHeight = 3x

According to the question, Total surface area of the Brick is 792 m².

Because the brick is in the shape of a cuboid because all the three measurements are distinct. And we know, Total surface area of cuboid is given by:

• TSA = 2(lb + bh + lh)

Where,

• l = Length, b = Breadth, h = Height

Substituting the value of l, b and h, we get

⇒ TSA = 792

⇒ 2 ( lb + bh + lh) = 792

⇒ lb + bh + lh = 396

⇒ x(2x) + 2x(3x) + x(3x) = 396

⇒ 2x² + 6x² + 3x² = 396

⇒ 11x² = 396

⇒ x² = 11

x = ± 11

∵ Length can't be negative, Hence x = -11 is neglected.

• So, x = 11

And we know, Volume of cuboid is given by

• Volume = l . b . h

⇒ Volume = l × b × h

⇒ Volume = 1x × 2x × 3x

⇒ Volume = 6x³

⇒ Volume = 6 (6)³

⇒ Volume = 1296 m³

Therefore, The correct option of this question is Option (A)

Answer 2

Answer:

Given :-

• A brick has length , breadth height in the ratio of 1 : 2 : 3 and total surface area of the brick is 792 sq m.

To Find :-

• What is the volume of the brick.

Formula Used :-

$\longmapsto \sf\boxed{\bold{\pink{Total\: Surface\: Area\: Of\: Cuboid =\: 2(LB + BH + HL)}}}$

$\longmapsto \sf\boxed{\bold{\pink{Volume\: Of\: Cuboid =\: L \times B \times H}}}$

where,

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

Solution :-

Let,

$\mapsto$ Length = x m

$\mapsto$ Breadth = 2x m

$\mapsto$ Height = 3x m

Now, according to the question by using the formula we get,

$\implies \sf 2(x \times 2x + 2x \times 3x + 3x \times x) =\: 792$

$\implies \sf 2(2{x}^{2} + 6{x}^{2} + 3{x}^{2}) =\: 792$

$\implies \sf 2(11{x}^{2}) =\: 792$

$\implies \sf 2 \times 11{x}^{2} =\: 792$

$\implies \sf 22{x}^{2} =\: 792$

$\implies \sf {x}^{2} =\: \dfrac{\cancel{792}}{\cancel{22}}$

$\implies \sf {x}^{2} =\: 36$

$\implies \sf x =\: \sqrt{36}$

$\implies \sf\bold{\green{x =\: 6 m}}$

Hence, the required length, breadth and height are :

➲ Length of the brick :

↦ $\sf x\: m$

➠ $\sf\bold{\purple{6\: m}}$

➲ Breadth of the brick :

↦ $\sf 2x\: m$

↦ $\sf 2(6)\: m$

↦ $\sf 2 \times 6\: m$

➠ $\sf\bold{\purple{12\: m}}$

And,

➲ Height of the brick :

↦ $\sf 3x\: m$

↦ $\sf 3(6)\: m$

↦ $\sf 3 \times 6\: m$

➠ $\sf\bold{\purple{18\: m}}$

Now, we have to find the volume of the brick :

Given :

• Length = 6 m
• Breadth = 12 m
• Height = 18 m

According to the question by using the formula we get,

$\implies \sf Volume\: Of\: Brick =\: 6\: m \times 12\: m\: \times 18\: m$

$\implies \sf Volume\: Of\: Brick =\: 72\: {m}^{2} \times 18\: m$

$\implies \sf \bold{\red{Volume\: Of\: Brick =\: 1296\: {m}^{3}}}$

$\therefore$ The volume of the brick is 1296 m³.

Hence, the correct options is option no (A) 1296 m³.