Question

How many hollow blocks of size $30{\text{cm}} \times 15{\text{cm}} \times 20{\text{cm}}$ are needed to construct a wall $60{\text{m}}$ in length, $0.3{\text{m}}$ in breadth and $2{\text{m}}$ in height?

Answer 1

Hint: Convert the units of wall from meter to centimeter to ease the calculation or we can convert the units of blocks from centimeter to meter but here we are converting the units of wall from meter to centimeter. Number of hollow blocks = $\dfrac{{{\text{Volume of wall}}}}{{{\text{Volume of one hollow block}}}}$ .

Complete step by step answer:
Given: Dimensions of hollow blocks of shape of cuboid are given as $30{\text{cm}} \times 15{\text{cm}} \times 20{\text{cm}}$. Also dimensions of wall shape of the cuboid are given as $60{\text{m}}$ in length, $0.3{\text{m}}$ in breadth and $2{\text{m}}$ in height.
As the hollow blocks are in the shape of cuboid therefore we will apply the formula of volume of cuboid here to find the volume of one hollow block.
Volume of cuboid $ = l \times b \times h$
Where $l = $ length of cuboid = 30 cm
$b = $ Breadth of cuboid = 15 cm
$h = $ Height of cuboid = 20 cm
Hence volume of one hollow block $ = 30{\text{cm}} \times 15{\text{cm}} \times 20{\text{cm}}$
$ = 9000{\text{c}}{{\text{m}}^3}$
Now we will find the volume of the wall with the same formula of volume of cuboid but first we convert the unit from meter to centimeter.
Length of wall $ = 60{\text{m}}$$ = 6000{\text{cm}}$
Because $1{\text{m}} = 100{\text{cm}}$
Similarly,
Breadth of wall $ = 0.3{\text{m}}$$ = 30{\text{cm}}$
Height of wall $ = 2{\text{m}}$$ = 200{\text{cm}}$
Volume of wall $ = $ length of wall $ \times $ breadth of wall $ \times $ height of wall
$
   = 6000{\text{cm}} \times 30{\text{cm}} \times 200{\text{cm}} \\
  {\text{ = 36000000c}}{{\text{m}}^3} \\
 $
Let ‘n’ be the total no. of hollow blocks needed to construct a wall.
Therefore, n$ \times $ volume of one hollow block $ = $ volume of wall
n$ \times $$9000{\text{c}}{{\text{m}}^3} = 36000000{\text{c}}{{\text{m}}^3}$
$
  {\text{n}} = \dfrac{{36000000}}{{9000}} \\
  {\text{n}} = 4000 \\
 $

Hence $4000$ hollow blocks are required to make a wall.

Note:
In these types of questions, always remember that the conversion volume remains the same. When all hollow blocks are combined total volume is equal to the volume of wall. Assume a number of blocks required as ‘n’ and multiply it by the volume of one block and it will be equal to the volume of the wall always.