Question

A wall of length 10m was to be built across an open ground. The height of the wall is 4m and the thickness of the wall is 24cm. If this wall is to be built up with bricks whose dimensions are \[24cm \times 12cm \times 8cm\], how many bricks would be required?

Answer 1

Hint:
A cuboid is a three-dimensional shape having six faces, eight vertices and twelve edges. The faces of the cuboid are parallel. In cuboids all the angles are at right angles. The three dimensions of cuboid are length, breadth and height. The volume of a three dimensional shape cuboid, is equal to the amount of space occupied by the shape. The volume of cuboid is given by the product of its dimensions.
Volume of the cuboid = (Length × Breadth × Height). Here, the bricks and walls are in the shape of cuboid. As the wall is made up of ‘n’ number of bricks, we can say that the volume of the wall is ‘n’ times the volume of brick. So, to find the number of bricks we have to first find the volume of the wall as well as the brick and we will use the formula given below in order to find the number of bricks.
While you are finding volume change metre into cm (or in same units). Use 1 metre = 100 cm
\[{\text{Number of bricks }} = \dfrac{{{\text{Volume of the wall}}}}{{{\text{Volume of one brick}}}}\]

Complete step by step solution:
According to the question
Dimension of the wall,
\[{\text{Length}} = 10m = 1000cm\]
\[{\text{Height}} = 4m = 400cm\]
\[{\text{and thickness}} = 24cm\]
\[\therefore {\text{Volume of the wall }} = {\text{ length}} \times {\text{breadth}} \times {\text{height}}\]
\[ = {\text{ 1000}} \times 400 \times 24c{m^3}\]
 (Since, wall is in shape of cuboid)
Dimension of a brick,
\[{\text{Length}}\left( l \right) = 24cm\]
\[{\text{Breadth(b)}} = 12cm\]
\[{\text{Height}}\left( h \right) = 8cm\]
\[\therefore {\text{Volume of one brick}} = {\text{l}} \times {\text{b}} \times {\text{h}}\]
\[ = 24 \times 12 \times 8c{m^3}\]
Now, to find the number of bricks
\[\therefore {\text{Number of bricks}} = \dfrac{{{\text{Volume of the wall}}}}{{{\text{Volume of one brick}}}}\]
\[ = \dfrac{{1000 \times 400 \times 24}}{{24 \times 12 \times 8}}\]
\[ = \dfrac{{1000 \times 50}}{{12}}\]
\[ = \dfrac{{25000}}{6}\]
\[ \cong 4166.66\]
\[{\text{Number of bricks}} = 4167\]

Note:
The volume of the cuboid is equal to the product of the area of one surface and height. So, if only the height and area is given then also we can find the volume, as it is the product of the area and height.