Question

Find the number of bricks, each measuring 25 cm x 12. 5 cm x 7. 5 cm required to construct a wall 6m long, 5m high and 0.5m thick, while the cement and sand mixture occupies \[\dfrac{1}{20}\] of the volume of the wall.

Answer 1

Hint: We will solve this question by finding the volume of bricks and wall and then substituting the values given in the question. The volume of cuboid is given by lbh, where l is the length of the brick, b the breadth of the brick and h is the height of the brick.

Complete step-by-step answer:
Given that, measures of brick = 25 cm x 12. 5 cm x 7. 5 cm
while the cement and sand mixture occupies \[\dfrac{1}{20}\] of the volume of the wall.
We have to calculate the number of bricks used.
Now because the wall is in the shape of a cuboid, we will use the formula of volume of cuboid which is given as V =lbh, where l is the length of the wall, b the breadth of the wall and h is the height of the wall.
Now we will all convert the given values from m to cm. Then,
6m of length will become 600 cm, 5m of height will become 500 cm and 0.5cm of breadth will become 50 cm.
Now we will find the volume of the wall by using the formula V = l x b x h
Substituting the values, we get,
Volume of the wall = \[(600)(500)(50)\]
\[\Rightarrow \]Volume = \[15000000c{{m}^{3}}\]
It is given that the volume of the mixture is \[\dfrac{1}{20}\] of the total mixture so the volume of the mixture is,
\[\Rightarrow \]Volume of the mixture = \[\dfrac{1}{20}(total\text{ }mixture)\]
\[\Rightarrow \]Volume of the mixture = \[\dfrac{1}{20}(15000000)\]
\[\Rightarrow \]Volume of the mixture = \[750000c{{m}^{3}}\]
Now the Volume of the remaining = \[15000000-750000\]
\[\Rightarrow \]The remaining volume in the wall =\[14250000c{{m}^{3}}\]
Now we will calculate the number of bricks required to make the wall which is obtained by dividing the remaining volume of the wall by the volume of one brick, which can be easily calculated by formula of volume of cuboid = lbh.
Therefore, the number of bricks required to make the wall = \[\dfrac{14250000c{{m}^{3}}}{(25)(12.5)(7.5)}\]
\[\Rightarrow \]No. of bricks required = \[\dfrac{14250000}{(25)(12.5)(7.5)}\]
 \[\Rightarrow \]No. of bricks required = \[\dfrac{14250000}{2343}\]
  \[\Rightarrow \]No. of bricks required = \[6080\]bricks
Therefore, the number of bricks required to make the wall is \[6080\].

Note: The possibility of error in this type of question can be at the point where we have to calculate the volume of the wall and the volume of the brick. Sometimes students may forget to subtract the volume of mixture and that will give us the wrong answer.