Answer

Verified

406.5k+ views

**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.

Recently Updated Pages

How many sigma and pi bonds are present in HCequiv class 11 chemistry CBSE

Mark and label the given geoinformation on the outline class 11 social science CBSE

When people say No pun intended what does that mea class 8 english CBSE

Name the states which share their boundary with Indias class 9 social science CBSE

Give an account of the Northern Plains of India class 9 social science CBSE

Change the following sentences into negative and interrogative class 10 english CBSE

Trending doubts

Which are the Top 10 Largest Countries of the World?

Fill the blanks with the suitable prepositions 1 The class 9 english CBSE

How do you graph the function fx 4x class 9 maths CBSE

The Equation xxx + 2 is Satisfied when x is Equal to Class 10 Maths

One Metric ton is equal to kg A 10000 B 1000 C 100 class 11 physics CBSE

Give 10 examples for herbs , shrubs , climbers , creepers

Differentiate between homogeneous and heterogeneous class 12 chemistry CBSE

Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE

Why is there a time difference of about 5 hours between class 10 social science CBSE