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A brick measures 20 cm by 10 cm by \[7\dfrac{1}{2}{\rm{cm}}\]. How many bricks will be required for a wall 25 m long, 2m high, \[\dfrac{3}{4}{\rm{m}}\] thick?

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Last updated date: 20th Jun 2024
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Answer
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Hint: Here we need to find the number of bricks. The shape of the bricks is of cuboids. So, we will first find the volume of each brick using the formula of the volume of cuboid. Then we will find the volume of the wall using the formula of the volume of cuboid. To find the number of bricks we will divide the volume of the wall by the volume of each brick. We will simplify it further to get the required number of bricks for a wall.

Formula Used:
We will use the formula of the volume of the cuboid is given by \[V = {\rm{length}} \times {\rm{width}} \times {\rm{height}}\].

Complete step by step solution:
Here we have to find the number of bricks required to construct a wall of the given dimensions.
It is given that the dimensions of each brick are 20 cm by 10 cm by \[7\dfrac{1}{2}{\rm{cm}}\].
Now, we will first find the volume of each brick using the formula of the volume of cuboid.
Substituting 20 for length, 10 for breadth and \[7\dfrac{1}{2}\] for height in the formula \[V = {\rm{length}} \times {\rm{width}} \times {\rm{height}}\], we get
 Volume of each brick \[ = 20 \times 10 \times 7\dfrac{1}{2}\]
Converting the mixed fraction into improper fractions, we get
\[ \Rightarrow \] Volume of each brick \[ = 20 \times 10 \times \dfrac{{15}}{2}\]
On multiplying the terms, we get
\[ \Rightarrow \] Volume of each brick \[ = 1500{\rm{c}}{{\rm{m}}^2}\] ………. \[\left( 1 \right)\]
Now, we will find the volume of the wall.
Before that we will first convert the units of dimensions of the wall in centimeters.
We know that \[1{\rm{m}} = 100{\rm{cm}}\]
Therefore, using this, we get
Length of wall \[ = 25{\rm{m}} = 25 \times 100{\rm{cm}} = 2500{\rm{cm}}\]
Height of wall \[ = 2{\rm{m}} = 2 \times 100{\rm{cm}} = 200{\rm{cm}}\]
Width of the wall \[ = \dfrac{3}{4}{\rm{m}} = \dfrac{3}{4} \times 100{\rm{cm}} = 75{\rm{cm}}\]
Now, we will find the volume of the wall using the formula of the volume of cuboid.
Substituting 2500 for length, 75 for breadth and 200 for height in the formula \[V = {\rm{length}} \times {\rm{width}} \times {\rm{height}}\], we get
Volume of the wall \[ = 2500 \times 200 \times 75\]
On multiplying the terms, we get
\[ \Rightarrow \] Volume of the wall \[ = 37,500,000c{m^2}\] ………. \[\left( 2 \right)\]
Now, we will find the number of bricks required which will be equal to the ratio of the volume of the wall to the volume of each brick.
Number of bricks required \[ = \dfrac{{37,500,000}}{{1500}}\]
On further simplification, we get
\[ \Rightarrow \] Number of bricks required \[ = 25,000\]

Hence, the number of bricks required to construct a wall of the given dimensions is equal to 25,000.

Note:
Here we have obtained the number of bricks required to construct a wall of given dimensions. Here we can make mistakes by multiplying the volume of the wall by the volume of brick instead of dividing and thus get a wrong answer. Also, the dimensions of walls are given in metres whereas the dimensions of bricks are given in centimetres. So, we need to keep the units of both the volumes the same, otherwise, we will get our answer wrong.