Question

a wall 15 metre long 30 cm wide and 4m high is made of bricks each measuring 22 cm × 12.5 cm × 7.5 CM if 1 by 12 of the total volume of the wall consist of mortar how many bricks are there in the wall ​

Answer 1

________________________

Answer-:

Total number of bricks required is 8000.

____________________________

Given-:

Dimensions of the wall are :

Length (l) = 1500cm

width(w)= 30cm

Height (h) = 400cm

_____________________________

Volume of the wall = (l*b*h)

=> (1500*30*400) cm²

=> (1500*12000) cm²

=> (180,00,000) cm²

_____________________________

According to Question-:

Volume of the Mortar

Volume of the Mortar = 1/12 of volume of wall

=> 1/12*180,00,000

=> 15,00,000 cm²

Total volume of only wall excluding the volume of mortar = (Total volume of wall -volume of mortar)

=> (180,00,000 - 15,00,000) cm²

=> 165,00,000 cm²

_____________________________

Now-:

Given dimensions of brick are :

length (L) = 22 cm

breath (b) = 12.5 cm

height (h) = 7.5 cm

Volume of bricks = (l*b*h)

=> (22*12.5*7.5) cm²

=> (2062.5) cm²

______________________________

Number of bricks = Volume of only wall/Volume of bricks

=> 165,00,000/2062.5

=> 8000

Therefore:-

Total number of bricks required is 8000.

Answer 2

Question :-

Given above ↑

Answer :-

→ Number of bricks = 800

To find :-

→ Number of bricks in wall .

Step - by - step explanation :-

Given that ,

• Length of wall (l) = 15 m
• Height of wall (h) = 4 m
• Width of wall ( b) = 0.3 m

Solution :-

The volume of wall(v) = l× b × h

$\implies \sf{ v \: = \red{15 \times 4 \times 0.3}} \\ \\ \implies \boxed{ \green{\sf{v \: = 18 \: {m}^{3} }}}$

_________________________________

Given that ,

$\star \ \sf{\green{volume \: of \: mortar(u)} = \frac{1}{12} \blue{ volume \: of \: wall}} \\ \\ \implies \sf{u \: = \frac{1}{12} \times 18} \\ \\ \implies \sf{ u \: = \frac{3}{2} } \\ \\ \implies \boxed{ \sf{\pink{u \: = 1.5 \: {m}^{3} }}}$

__________________________________

Now ,

Total volume excluding the volume of

mortar(m) = (v) - (u) [ volume of wall - volume of mortar ]

$\implies \sf{m \: = 18 - 1.5} \\ \\ \implies \boxed{ \sf{\green{ m \: = 16.5 \: {m}^{3} } \: }}$

___________________________________

Given that ,

We takes all dimensions of wall and bricks in metre.

• Length of bricks (a) = 0.22 m
• height of bricks (b) = 0.075 m
• breadth of bricks (c) = 0.125 m

Therefore ,

Volume of bricks(k) = a × b × c

$\implies \sf{ k \: =\red{ 0.22 \times 0.075 \times 0.125 \: {m}^{3}} } \\ \\ \implies \boxed{ \sf{k \: = 0.0020625 \: {m}^{3} }} \\ \\ or \\ \\ \implies \boxed{ \sf{\green{k \: = 2062.5 \: {(cm)}^{3}} }}$

__________________________________

Now ,

$\boxed{\sf{\red{number \: of \: bricks }= \frac{\green{volume \: of \: wall(m)}}{\blue{volume \: of \: bricks(k)}} }} \\ \\ \implies \sf{ \frac{16.5}{0.0020625} } \\ \\ \implies \: 8000$

Hence ,

Total number of bricks required is 800.

__________________________________