Question

A mason constructs a wall of dimensions \[270{\text{ }}cm\; \times {\text{ }}300{\text{ }}cm{\text{ }} \times {\text{ }}350{\text{ }}cm\]with the bricks each of size \[22.5{\text{ }}cm{\text{ }} \times {\text{ }}11.25{\text{ }}cm\; \times {\text{ }}8.75{\text{ }}cm\] and it is assumed that \[\dfrac{1}{8}\] space is covered by the mortar. Then, the number of bricks used to construct the wall is
A) 11100
B) 11200
C) 11000
D) 11300

Answer 1

Hint: Calculating the Bricks Required in a Wall:- The required data for calculating the bricks are:
Volume of wall
Details of opening in the wall
Volume of a standard brick
The procedure of calculating the bricks are:
Volume of Wall
Calculate the dimension of the wall. The dimension of the wall includes length L, height H, and thickness W.
Multiply all dimensions with each other $L \times H \times W$. You will get the volume of the wall.
Volume of wall $V$ = $L \times H \times W$
Openings in the Wall
Examples of openings in a wall are door & windows etc.
Calculate the volume $L \times H \times W$ of the opening (door or window) in the wall
Subtract it from the volume of the wall
V = Volume of the wall – Volume of the opening
Number of Bricks
Calculate the volume $L \times H \times W$ of the brick, we are going to divide the volume of the wall with Volume of the bricks to get the number of bricks.

Complete step-by-step answer:
To find the answer to this question first you will need to calculate:
Cuboid is a solid box whose every surface is a rectangle of the same area or different areas.
A cuboid will have a length, breadth and height.
Volume of a cuboid = \[\left( {length{\text{ }} \times {\text{ }}breadth{\text{ }} \times {\text{ }}height} \right)\] cubic units.
The length of the cuboid = 270 cm
The breadth of the cuboid = 300 cm
The height of cuboid = 350 cm
The number of 1 cm cubes in the given cuboid = 28350000 cubes = $270 \times 300 \times 350$
The entire volume of the wall
= \[270{\text{ }}cm\; \times {\text{ }}300{\text{ }}cm{\text{ }} \times {\text{ }}350{\text{ }}cm\]
= 28350000 cm³
We find that the volume of the given cuboid with length 270 cm, breadth 300 cm and height 350 cm is 283500000 cu cm.
If the mortar covers a space of \[\dfrac{1}{8}\] then the bricks covers a volume of \[\dfrac{7}{8}\]
That is \[\dfrac{7}{8}\]of 28350000 = 24806250 cm³
Next step: Find the volume of each brick
\[22.5cm{\text{ }} \times {\text{ }}11.25cm{\text{ }} \times {\text{ }}8.75cm\] = 2214.84375
Divide the total volume by the volume of the bricks to find the number of bricks used:
\[ \Rightarrow \dfrac{{24806250}}{{2214.84375}}{\text{ }} = {\text{ }}11200{\text{ }}bricks\]
That is a total of 11200 bricks used to construct the wall in the mansion.

So, option (B) is the correct answer.

Note: In this question two parameters are not given which you may consider in the next similar question you are attempting.
Wastage of bricks. So, you have to add the percentage of wastage of bricks in total number of bricks if given
If the wall has any openings such as doors, windows etc subtract the volume of the opening from the volume of the wall and then divide it by the volume of brick.