Question

How many bricks will be required for a wall which is 8m long, 6m high and 22.5 cm thick, if each brick measures $25cm\times 11.25cm\times 6cm$?

Answer 1

Hint: In this question, we are given dimensions of a wall and dimension of a brick. As we know, bricks will occupy the space of the wall (they create the wall) therefore, the volume of all bricks will be equal to the volume of the wall. So to solve this question, we will first find the volume of the wall and then the volume of a single brick. For finding the number of bricks required, we will divide the volume of the wall by volume of one brick. Since, wall and brick both are cuboid so, formula to find volume of cuboid is given by $l\times b\times h$ where, l is length, b is breadth and h is height.

Complete step by step answer:
Dimensions of wall are as follows:
Length of wall is equal to 8m.
Breadth of wall is equal to 22.5cm and
Height of the wall is equal to 6m.
Since units of breadth are different from that of length and height, let us change units of length and height from meters to centimeters.
As we know, 1m = 100cm. Therefore,
$8m=8\times 100=800cm\text{ and 6}m=6\times 100=600cm$.
Thus, for wall l = 800cm, b = 22.5cm and h = 600cm.
Let us now find the volume of the wall.
Since the wall is in shape of cuboid and volume of cuboid is given by $l\times b\times h$ therefore, volume of wall becomes equal to $l\times b\times h$. Putting value of l, b and h we get:
\[\begin{align}
  & \text{Volume of wall}=800\times 22.5\times 600 \\
 & \Rightarrow 10800000c{{m}^{3}} \\
\end{align}\]
Dimensions of brick are as follows:
Length of brick is equal to 25cm.
Breadth of brick is equal to 11.25cm and
Height of the brick is equal to 6cm.
Therefore, l = 25cm, b = 11.25cm and h = 6cm.
Let us now find the volume of one brick. Since, brick is in the shape of cuboid and volume of cuboid is given by $l\times b\times h$ therefore, volume of brick becomes equal to $l\times b\times h$. Putting values of l, b and h we get:
\[\begin{align}
  & \text{Volume of brick}=25\times 11.25\times 6 \\
 & \Rightarrow 1687.5c{{m}^{3}} \\
\end{align}\]
Let n number of bricks make the wall.
Since, bricks will occupy space of wall (they make it) hence, volume of wall will be equal to volume of n bricks.
\[\text{Volume of wall}=\text{Volume of one brick}\times \text{n}\]. Therefore,
\[\text{n}=\dfrac{\text{Volume of wall}}{\text{Volume of one brick}}\]
Putting values found earlier, we get:
\[\begin{align}
  & \text{n}=\dfrac{\text{10800000c}{{\text{m}}^{\text{3}}}}{\text{1687}\text{.5c}{{\text{m}}^{\text{3}}}} \\
 & \Rightarrow \text{n}=\dfrac{\text{108000000}}{\text{16875}} \\
 & \Rightarrow n=6400 \\
\end{align}\]
As n was supposed to be the number of bricks.

Number of bricks required to make wall = 6400.

Note: Students should note that units of all dimensions should be the same. While dividing also, the unit of volume of wall and unit of volume of brick should be the same. Students should keep in mind the formula for finding volumes of all the dimensional shapes.