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​

Answer 1

Explanation:

this is the answer of the question

Answer 2

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.

To Find:-

• Find the volume of the brick.

Solution:-

As we know that:-

• TSA = 2( lb + bh + lh )

$\longrightarrow\sf \: TSA = 729$

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

$\longrightarrow\sf \: \cancel\dfrac { 792 } { 2 } = { 2x }^{ 2 } + { 6x }^{ 2 } + { 3x }^{ 2 }$

$\longrightarrow\sf \: 396 = { 11x }^{ 2 }$

$\longrightarrow\sf \:  { x }^{ 2 } = \dfrac { 396 } { 11 }$

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

$\longrightarrow\sf \: x = 6$

Then ,

• Length of brick is x = 6 m

• Breadth of brick is 2x = 12 m

• Height of brick is 3x = 18 m

Now ,

We have to find volume of Cuboid:-

$\longrightarrow\sf \: 6 \times 12 \times 18$

$\longrightarrow\sf \: 1296 \: { m }^{ 3 }$

Hence ,

• Volume is $\sf \: 1296 \: { m }^{ 3 }$