Question

44. How many bricks, each measuring 30 cm x 20 cm 5 cm will be needed to construct a wall 10 m lon 6 m high and 12 cm thick?​

Answer 1

Given :

• The dimensions of Brick = 30 cm, 20 cm, and 5 cm.
• The dimensions of Wall = 10 m, 6 m, and 12 cm.

To find :

• how many bricks are needed to construct the wall?

Solution :

⇒ Let's find the Volume of the Brick.

The volume of the brick = l × b × h

= 30 × 20 × 5

= 30 × 100

= 3000 cm³

⇒ Let's find the Volume of the Wall.

• Here, before finding the Volume, we have to convert the length and breadth from cm to m.

→ 10 m to cm.

1 m = 100 cm

10 m = 10 × 100

= 1000 cm

→ 6m to cm.

1 m = 100 cm

6 m = 6 × 100

= 600 cm

The volume of the wall = l × b × h

= 1000 × 600 × 12

= 600000 × 12

= 7200000 cm³

⇒ Now, let's find how many bricks are needed.

No of bricks = Volume of Wall/Volume of Brick

= 7200000/3000

= 2400

• Therefore, 2400 bricks are required to construct a wall.

Answer 2

$\underline{\underline{\sf{\maltese\:Given:-}}}$

$\qquad\sf{:\implies\:The\: dimensions\: of\: Brick\: = \:30 \:cm\:,\: 20 \:cm\:,\: and \:5\: cm\:.}$

$\qquad\sf{:\implies\:The\: dimensions\: of \:Wall\: =\: 10\: m\:,\: 6 \:m\:,\: and \:12\: cm.}$

$\underline{\underline{\sf{\maltese\:To\:find:-}}}$

$\qquad\sf{:\implies\:How\: many\: bricks\: are \:needed \:to\: construct \:the\: wall\:}$

$\underline{\underline{\sf{\maltese\:Concept:-}}}$

$\odot$ Here we give that the dimensions of Brick are 30 cm, 20 cm, and 5 cm and  the dimensions of the Wall are 10 m, 6 m, and 12 cm. so firstly we will find out the volume of the bricks.

$\odot$ After finding the volume of the bricks we will find out the volume of the wall.  so firstly we will convert meters to centimetres and then we will substitute the values in the formula to find out the volume of the wall.

$\odot$ After finding the volume of the wall we will find out how many bricks are needed to construct the wall.

$\underline{\underline{\sf{\maltese\:Full \:Solution:-}}}$

~Let us find out the volume of the bricks by substituting the given values in the formula ( Volume of the bricks = l × b × h ).

$\sf{:\implies\:Volume\:of\:the\:bricks\:=\:l\:\times\:b\:\times\:h}$

$\sf{:\implies\:Volume\:of\:the\:bricks\:=\:30\:\times\:20\:\times\:5}$

$\sf{:\implies\:Volume\:of\:the\:bricks\:=\:600\:\times\:5}$

$\sf{:\implies\:Volume\:of\:the\:bricks\:=\:3000\;cm^{3}}$

Hence the volume of the bricks is 3000 cm³.

$\qquad\qquad\underline{\qquad\qquad\qquad\qquad\qquad}$

~Let us convert the values metres to centimetres.

1) 10m → cm

$\qquad\sf{:\implies\:1\:m\:→\:100\:cm}$

$\qquad\sf{:\implies\:10m\:→\:10\:\times\:100}$

$\qquad\sf{:\implies\:1000\:cm}$

2) 6m → cm

$\qquad\sf{:\implies\:1\:m\:→\:100\:cm}$

$\qquad\sf{:\implies\:6m\:→\:6\:\times\:100}$

$\qquad\sf{:\implies\:600\:cm}$

$\qquad\qquad\underline{\qquad\qquad\qquad\qquad\qquad}$

~Let us find out the volume of the wall by substituting the values in the formula ( volume of the wall = l × b × h ).

$\qquad\sf{:\implies\:Volume \:of\: the\: wall\: =\: l\: \times\: b\: \times \:h}$

$\qquad\sf{:\implies\:Volume \:of\: the\: wall\: =\: 1000\: \times\: 600\: \times \:12}$

$\qquad\sf{:\implies\:Volume \:of\: the\: wall\: =\: 600000\: \times \:12}$

$\qquad\sf{:\implies\:Volume \:of\: the\: wall\: =\: 7200000\:cm^{3}}$

Hence the volume of the wall is 7200000 cm³.

$\qquad\qquad\underline{\qquad\qquad\qquad\qquad\qquad}$

~Let us find out how many bricks are needed to construct the wall by dividing the volume of the bricks by volume of walls.

$\qquad\sf{:\implies\:Number\:of\:bricks\:=\:\dfrac{Volume\:of\:the\:wall}{Volume\:of\:the\:bricks}}$

$\qquad\sf{:\implies\:Number\:of\:bricks\:=\:\dfrac{7200000}{3000}}$

$\qquad\sf{:\implies\:Number\:of\:bricks\:=\:\dfrac{7200}{3}}$

$\qquad\sf{:\implies\:Number\:of\:bricks\:=\:2400}$

Hence we need 2400 bricks to construct a wall.

$\qquad\qquad\underline{\qquad\qquad\qquad\qquad\qquad}$