Question

Q - 1) A wall of length 10m was to be built across an open ground. The height of the wall is 4 m and thickness of the wall is 24 cm. If this wall is to be built up with bricks whose dimensions are 24cm × 12 cm × 8 cm, how many bricks would be required ??


Q - 2) The pillars of a temple are cylindrically shaped. If each pillar has a circular base of radius 20 cm and height 10m, how much concrete mixture would be required to build 14 such pillars ??​

Answer 1

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${ \mathtt{ \huge{ \underline{ \pink{Answer ( 1 )}}}}}$

${ \bf{ \underline{ \green{Given :-}}}}$

• Length = 10 m
• Thickness = 24 cm
• Height = 4 m

${ \bf{ \underline{ \purple{To \: find :-}}}}$

• How many bricks would be required ??

${ \bf{ \underline{ \red{Solution :-}}}}$

↬ Since the wall with all its bricks makes up the space occupied by it, we need to find the volume of the wall, which is nothing but a cuboid

$●{ \rm{Length \: = 10 \: m \: = 1000 \: cm}}$

$●{ \rm{Thickness = 24cm}}$

$●{ \rm{Height = 4m = 400cm}}$

${ \rm{Volume \: of \: the \: wall = length \times thickness \times height}}$

${ \rm{1000 \times 24 \times 400 \: cm {}^{3} }}$

Now, Each brick is a cuboid with length = 24cm, breadth = 12cm, Height = 8cm

${ \rm{Volume \: of \: each \: brick = Length \times breadth \times height}}</p><p>${ \rm{24 \times 12 \times 8 \: cm {}^{3}}} [/tex]

${ \rm{So, \: Number \: of \: bricks \: required \: = \frac{volume \: of \: the \: wall}{volume \: of \: each \: brick} }}$

${ \rm{ \frac{1000 \times 24 \times 400}{24 \times 12 \times 8} = 4166.6}}$

${ \rm{So, \: the \: wall \: requires \: { \boxed{ \blue{ \rm{4167 }}}\: bricks}}}$

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${ \mathtt{ \huge{ \underline{ \pink{Answer ( 2 )}}}}}$

${ \bf{ \underline{ \green{Given :-}}}}$

• Radius of base of cylinder = 20 cm
• Height of the cylindrical pillar = 10 m

${ \bf{ \underline{ \purple{To \: find :-}}}}$

• how much concrete mixture would be required to build 14 such pillars ??

${ \bf{ \underline{ \red{Solution :-}}}}$

↬Since, the concrete mixture that is to be used to build up the pillars is going to occupy the the entire space of the pillar, what we need to find hair is the volume of the cylinders.

• Radius of the cylindrical pillar = 20 cm
• Height of the cylindrical pillar = 10m = 1000cm

${ \rm{We \: know \: that, }}$

${ \boxed{ \orange{ \rm{Volume \: of \: cylinder = \pi \: r {}^{2} h}}}}$

${ \rm{ \frac{22}{7} \times 20 \times 20 \times 1000 \: cm {}^{3} }}$

${ \rm{ \frac{8800000}{7} cm {}^{3} }}$

${ \rm{ \frac{8.8}{7} m {}^{3} (since1000000 \: cm {}^{3} = 1 \: m {}^{3} )}}$

${ \rm{Volume \: of \: 14 \: pillars =volume \: of \: each \: cylinder \times 14}}$

${ \rm{ \frac{8.8}{7} \times 14m {}^{3} = 17.6 \: m {}^{3}}}$

${ \rm{So, \: 14 \: pillars \: would \: need \: { \boxed{ \blue{ \rm{ 17.6 m³}}}} of \: concrete \: mixture}}</p><p>$

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Answer 2

$\large\purple{\boxed{\rm{Answer⤵}}}$

Question 1 :-

Length = 1000cm

Thickness = 24cm

Height = 4000cm

Volume of wall

Volume = Length × Thickness × Height

Volume = 1000 × 24 × 4000

Volume of each brick

Volume of each brick = Length × Breadth × Height

Volume of each brick = 24 × 12 × 8

$\large\rm number \: of \: bricks \: required = \frac{volume \: of \: wall}{volume \: of \: each \: brick}$

$\large\rm \frac{1000 \times 24 \times 400}{24 \times 12 \times 8}$

$\large\pink{\boxed{\rm{Number\: of\: bricks=4167\: bricks}}}$

Question 2 :-

Radius of pillar = 20cm

Height of pillar = 1000cm

Volume = $\large\rm volume = 2\pi{r}^{2}$

$\large\rm \frac{22}{7} \times 20 \times 20 \times 1000$

$\large\rm \frac{8.8}{7} {m}^{3}$

Volume of 14 pillars = Volume of each cylinder × 14

$\large\rm \frac{8.8}{7} \times 14$

$\large\orange{\boxed{\rm{Volume\: of\: pillars=17.6m³}}}$