Question

To construct a wall 25m long, 0.3m thick and 6m high, bricks of dimensions 50cm * 15cm *
10cm, each are used. If the mortar occupies 1/10th of the volume of the wall, find the number
of bricks used?​

Answer 1

$\small \text{Dimension of wall = 25 m × 0.3 m × 6 m}$

$\small \text{Dimension of brick = 50 cm × 15 cm × 10 cm}$

• Mortar fit in the wall occupies 1/10 part of wall's volume.

Here,

$\text{Volume of wall} = (25 \times \frac{3}{10} \times 6) \\ \\ = > (25 \times 6) \times \frac{3}{10} \\ \\ = > 15\cancel0 \times \frac{3}{1 \cancel0} \: \: = 45 \: \: \rm{cm}^{3}$

$\text{Volume of brick} = (50 \times 15 \times 10) \\ \\ = >( 50 \times 10) \times 15 \\ = > 500 \times 15 = 7500 \: \: \rm {cm}^{3}$

• 1 m³ = 10⁶ cm³
• 1 cm³ = 1/10⁶ m³

$\leadsto 7500 \: \: \rm {cm}^{3} \\ \\ \: \huge\bf{Or,} \\ \\ \leadsto \frac{7500}{ {10}^{6} } \: \: \rm {m}^{3} \: \: \: \: \: \: \: \{ Or, \} \: \: \: \: \: \: \tt \frac{75}{ {10}^{4} } \: \: {m}^{3}$

Now,

Volume of wall occupied by mortar = 45 × 1/10

• => 4.5 m³

i.e. 4.5 m³ of wall has mortar.

So,

(45 - 4.5) m³ of wall's volume has bricks in them.

i.e. 40.5 m³ of wall contain bricks.

Therefore,

$\large \text{Number of bricks in the wall} \\ \\ \small = > \frac{ \text{Volume of wall which contain brick}}{ \text{Volume of each brick}} \\ \\ \tt = > \frac{40.5}{ \frac{75}{ {10}^{4} } } \\ \\ = > \frac{40.5}{75} \times {10}^{4} \\ \\ = > \frac{405}{75 \times 10} \times {10}^{4} \\ \\ = > \frac{5.4}{10} \times {10}^{4} \\ \\ = > 5.4 \times {10}^{3} \\ = > 5400 \: \:$

Hence,

• The wall contain 5400 bricks.