Question

how many bricks each measuring 25 cm * 15 cm * 8 cm will be required to build a wall 10 m * 4 m * 5 m when
$\frac{1}{10} of its volume is occupied by mortar$
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Answer 1

Given -

• Dimensions of brick = 25cm × 15cm × 8cm

• Dimensions of wall = 10m × 4m × 4m

To find -

• Number of bricks required.

Formula used -

• Volume of cuboid = l × b × h

Solution -

In the question, we are given with the dimensions of wall and the dimensions of brick, and we need to find out the bricks required to build the wall. For that first we will find the volume of wall and the volume of brick, after that we will divide the volume of wall and the volume of brick, that will give us the total number of bricks.

According to question -

Length of wall = 10m

Breadth of wall = 4m

Height of wall = 5m

And -

Length of brick = 25cm

Breadth of brick = 15cm

Height of brick = 8cm

Now -

We first we will find the volume of wall, by using the formula of volume of cuboid. And then we will multiply it with the $\sf\frac{1}{10}$ .

Volume of cuboid = l × b × h

where -

l = Length

b = Breadth

h = Height

On substituting the values -

$\sf \longrightarrow \: v \: = l \: \times \: b \: \times \: h \\ \\ \\ \sf \longrightarrow \: v \: = 10m \: \times \: 4m \: \times \: 5m \: \\ \\ \\ \sf \longrightarrow \: v \: = 200 {m}^{3}$

Now -

We will multiply it with the $\sf\frac{1}{10}$, to find the volume left of that wall.

$\sf \longrightarrow \: v \: = 200 {m}^{3} \\ \\ \\ \sf \longrightarrow \: space \: occupied \: by \: motor \: = \dfrac{1}{10} \: \times \: 200 \\ \\ \\ \sf \longrightarrow \: space \: occupied \: by \: motor \: = 20 {m}^{3} \\ \\ \\ \sf \longrightarrow \: volume \: left \: = 200 \: - \: 20 \: = 180 {m}^{3}$

Now -

We will find the volume of bricks by again applying the formula of volume of cuboid.

$\sf \longrightarrow \: v \: = l \: \times \: b \: \times \: h \\ \\ \\ \sf \longrightarrow \: v \: = 25cm \: \times \: 15cm \: \times 8cm \: \\ \\ \\ \sf \longrightarrow \: v \: = 3000 {cm}^{3} \\ \\ \\ \sf \longrightarrow \: v \: = 0.003 {m}^{3}$

At the end -

We will find the number of bricks by dividing the volume of wall by the volume of brick.

$\sf \longrightarrow \: no._{(of\:bricks)} \: = \dfrac{volume \: of \: wall}{volume \: of \: brick} \\ \\ \\ \sf \longrightarrow \: no._{(of\:bricks)} \: = \dfrac{180}{0.003} \\ \\ \\ \sf \ \longrightarrow no._{(of\: bricks)} \: = 60000$

$\therefore$ 60000 bricks will be required to make the wall.

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Answer 2

◐ Given :–

• Dimensions of a brick = 25 cm × 15 cm × 8 cm.

• Dimensions of the wall = 10 m × 4 m × 5 m.

• $\dfrac{1}{10}$ of its volume is occupied by mortar.

◐ To Find :–

• The number of bricks required to build the wall.

◐ Solution :–

» We would first find the volume of a brick.

» Then, we would find the volume of the wall.

» Since ${\dfrac{1}{10}}^{th}$ of the volume is occupied by the mortar, so, we would find the remaining volume.

» After finding the remaining volume, we would divide it by the volume of a brick so as to get the number of bricks.

◆ Finding the Volume of a Brick :

We have :

• Length = 25 cm
• Breadth = 15 cm
• Height = 8 cm

We know -

$\odot\;\boxed{\sf Volume_{\:cuboid}=Length\times Breadth \times Height }$

So,

$\colon \rarr \sf \: volume _{ \: brick} = 25 \times 15 \times 8 \: {cm}^{3} \\ \\ \colon \dashrightarrow \boxed{ \pink{\frak{volume _{ \: brick} = 3000 \: {cm}^{3} }}}$

◆ Finding the Volume of the Wall :

We have :

• Length = 10 m = 1000 cm
• Breadth = 4 m = 400 cm
• Height = 5 m = 500 cm

So,

$\colon \rarr \sf \: volume _{ \: wall} = 1000 \times 400 \times 500 \: {cm}^{3} \\ \\ \colon \dashrightarrow \boxed{ \frak{ \pink{volume _{ \: wall} = 200000000 \: {cm}^{3}}}}$

◆ Finding Remaining Volume :

We have :

• Volume of the wall = 20,00,00,000 cm³

• $\dfrac{1}{10}$ of the volume is occupied by mortar.

So,

$\colon \rarr \sf \: remaining \: volume = volume _{ \: wall} - \frac{1}{10} \times volume _{ \: wall} \\ \\ \colon \rarr \sf \: remaining \: volume = \frac{9}{10} \times volume _{ \: wall} \\ \\ \colon \sf \rarr \: remaining \: volume = \frac{9}{ \cancel{10}} \times 20000000 \cancel0 \: {cm}^{3} \\ \\ \colon \rarr \boxed{ \pink{ \frak{remaining \: volume = 180000000 \: {cm}^{3}}}}$

◆ Finding the Number of Bricks :

We have :

• Volume of brick = 3000 cm³
• Remaining Volume of wall = 18,00,00,000 cm³

So,

$\colon \rarr \sf \: no. \: of \: bricks = \frac{ remaining \: volume }{volume _{ \: brick} } \\ \\ \colon \sf \rarr \: no. \: of \: bricks = \frac{180000 \cancel{000}}{3 \cancel{000} } \\ \\ \colon \rarr \sf \: no. \: of \: bricks = \cancel \frac{180000}{3} \\ \\ \colon \dashrightarrow \underline{ \boxed { \frak{ \red{no. \: of \: bricks = 60000}}}}$

$\therefore\;\underline{\sf The\:Number\:of\:bricks\:required\:to\:build\:the\:wall\:is\:\bf{6000.}}$

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