Question

A wall 24 m long, 0.4 m thick and 6 m high is constructed with the bricks each of dimensions 25 cm × 16 cm × 10 cm. If the mortar occupies `1/10` th of the volume of the wall, then find the number of bricks used in constructing the wall.

Answer 1

Given that, a wall is constructed with the help of bricks and mortar.

∴ Number of bricks = `(("Volume of wall") - (1/10 "th volume of wall"))/"Volume of a brick"`  ...(i)

Also, given that

Length of a wall (l) = 24 m,

Thickness of a wall (b) = 0.4 m,

Height of a wall (h) = 6 m

So, volume of a wall constructed with the bricks = l × b × h

= 24 × 0.4 × 6

= `(24 xx 4 xx 6)/10 "m"^3`

Now, `1/10`th volume of a wall

= `1/10 xx (24 xx 4 xx 6)/10`

= `(24 xx 4 xx 6)/10^2 "m"^3`

And length of a brick (l₁) = 25 cm = `25/100 "m"`

Breadth of a brick (b₁) = 16 cm = `16/100 "m"`

Height of a brick (h₁) = 10 cm = `10/100 "m"`

So, volume of a brick = l₁ × b₁ × h₁

= `25/100 xx 16/100 xx 10/100`

= `(25 xx 16)/10^5 "m"^3`

From equation (i),

Number of bricks = `(((24 xx 4 xx 6)/10 - (24 xx 4 xx 6)/100))/(((25 xx 16)/10^5)`

= `(24 xx 4 xx 6)/100 xx 9 xx 10^5/(25 xx 16)`

= `(24 xx 4 xx 6 xx 9 xx 1000)/(25 xx 16)`

= 24 × 6 × 9 × 10

= 12960

Hence, the required number of bricks used in constructing the wall is 12960.