Question

How many prices, each measuring \[25cm\times 12.5cm\times 7.5cm\] will be needed to construct a wall 15 m long, 1.8 m high and 37.5 cm thick?

Answer 1

Hint: We will find the volume of the wall as well as the volume of brick and then we will divide the volume of wall by volume of the brick. Hence we will get the required number of bricks to construct the wall of given dimension. We will use the formula to find the volume is as follows:
Volume \[=l\times b\times h\] where l, b and h are length, breadth and height.

Complete step-by-step answer:
We have been asked to find the number of bricks each measuring \[25cm\times 12.5cm\times 7.5cm\] to construct a wall 15 m long, 1.8 m high and 37.5 m thick. Let us consider the figures as below,

Since we know that the volume of the brick \[=l\times b\times h\] when l, b and h are length, breadth and height respectively.
We have \[l=25cm,b=12.5cm,h=7.5cm\]
So volume of brick \[=\left( 25\times 12.5\times 7.5 \right)c{{m}^{3}}=2343.75c{{m}^{3}}\]
Similarly, for the wall we have \[l=15m,b=37.5cm,h=1.8m\]
We will have to convert ‘cm’ into ‘m’ using the relation, \[1cm=\dfrac{1}{100}m\].
\[\Rightarrow b=\dfrac{37.5}{100}m=0.375m\]
Now the volume of wall \[=15\times 0.375\times 1.8=10.125{{m}^{3}}\]
Now we will have to convert volume of brick from unit \[c{{m}^{3}}\] to \[{{m}^{3}}\] by using the relation \[1c{{m}^{3}}={{10}^{-6}}{{m}^{3}}\].
\[\Rightarrow \]Volume of brick \[=2343.75\times {{10}^{-6}}{{m}^{3}}\]
We can find the number of bricks by dividing the volume of the wall by the volume of one brick. So, we get
Number of bricks \[=\dfrac{volume\text{ }of\text{ }wall}{volume\text{ }of\text{ }brick}=\dfrac{10.125}{2343.75\times {{10}^{-6}}}=4320\]
Therefore, the required number of bricks to construct the wall is equal to 4320.

Note: Be careful while doing calculation and remember that all units must be the same. Sometimes by mistake we forget to change units and we get the wrong answer. We will have to change the units of volume of bricks from \[c{{m}^{3}}\] to \[{{m}^{3}}\] and also the unit of thickness of wall from cm to m.