Question

3. The pillars of a temple are cylindrically shaped. Each pillar has a
circular base of radius 20 cm and height 10 m. How much concrete
mixture would be required to build 14 such pillars?​

Answer 1

Step-by-step explanation:

Considering it to a solid cylinder, for amount of concrete making are cylinder = volume of cylinder

∴ Amount of concrete mixture required to fild 14 such pillars =14× volume of a cylinder−−−−−(1)

If Volume of cylinder where =πr

2

h

x=radius

h=height

Volume =π×x

2

×h

=π×20×20×10 cm

3

=4000π cm

3

=4000×3.142 cm

3

=12568 cm

3

Substituting it in equation (1)

=14×12568

=150816 cm

3

∴ Amount of concrete mixture required to build 14 such pillars =150816 cm

3

Answer 2

$\pink\bigstar{ \underline { \underline { \bf{↬ \purple{GiVeN}↫}}}} \green \bigstar$

$✪ \small \sf Radius \: of \: one \: pillar ,r \longrightarrow \: 20cm \\ \small \sf \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \longrightarrow \frac{2 \cancel0}{10 \cancel0} m \\ \small \sf \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \longrightarrow \boxed{ \bf .2m}$

$✪ \small \sf Height \: of \: one \: pillar,h \longrightarrow \: \boxed { \bf 10 \: m}$

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$\pink\bigstar{ \underline { \underline { \bf{↬ \purple{ To \: FiNd}↫}}}} \green \bigstar$

$✪ \small \sf Volume \: of \: one \: cylindrical \: pillar \: \: \: \: \: \: \: \: \: \\ ✪ \small \sf Volume \: of \: 14 \: cylindrical \: pillars \: \: \: \: \: \: \: \: \: \\ ✪ \small \sf Concrete \: mixture \: to \: build \: 14 \: pillars \:$

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$\pink\bigstar{ \underline { \underline { \bf{↬ \purple{ ForMuLa \: ReQuiReD}↫}}}} \green \bigstar$

$\small \bigstar { \underline{\boxed{ \bf Volume \: of \: a \: Cylinder \: \leadsto \pi {r}^{2} h}} } \bigstar$

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$\pink\bigstar{ \underline { \underline { \bf{↬ \purple{SoLuTioN}↫}}}} \green \bigstar$

$\small \sf \therefore{Volume \: of \: one \: Cylindrical \: pillar ➛ \pi {r}^{2} h}$

$\small \implies\sf {Volume \: of \: one \: Cylindrical \: pillar ➛ \frac{22}{7} \times .2 \times .2 \times 10 \: m {}^{3} }$

$\small \sf \implies {Volume \: of \: one \: Cylindrical \: pillar ➛ \frac{22 \times .04 \times 10}{7}m {}^{3} }$

$\small \sf \implies{Volume \: of \: one \: Cylindrical \: pillar ➛ \frac{220 \times .04}{7} {m}^{3} }$

$\small \sf \implies {Volume \: of \: one \: Cylindrical \: pillar ➛ \frac{8.80}{7} \: m {}^{3} }$

$\small \sf \therefore{Volume \: of \: 14 \: Cylindrical \: pillar ➛ \cancel{ 14} \times \frac{8.80}{ \cancel7} }$

$\small \sf \implies{Volume \: of \: one \: Cylindrical \: pillar ➛2 \times 8.80 \: m {}^{3} }$

$\small \sf \implies{Volume \: of \: 14 \: Cylindrical \: pillar ➛ 17.60 \: {m}^{3} }$

$\small \sf \implies{Volume \: of \: 14\: Cylindrical \: pillar ➛ 17.6 \: { m}^{3} }$

$\small \sf \therefore \: Concrete\: mixture \: to \: build \: 14 \: pillars \longrightarrow {\boxed{ \bf {17.6 \: {m}^{3} }}}$

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$\pink\bigstar{ \underline { \underline { \bf{↬ \purple{AnaLySis}↫}}}} \green \bigstar$

$\small \bf \: Here,we \: have \: to \: find \: the \: quantity \: \: \: \: \: \: \: \: \: \: \: \: \\ \small \bf of \: concrete \: mixture \: to \: build \: 14 \: pillars \: \: \: \: \\ \small \bf \:We \: will \: used \: the \: formula \: \leadsto\: Volume \: of \\ \small \bf\: a \: cyclinder$

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$\pink\bigstar{ \underline { \underline { \bf{↬ \purple{StePs}↫}}}} \green \bigstar$

• Firstly, here we have converted the unit ( cm into m ) so that both are of same units.

• Then , we have applied the formula - Volume of a cyclinder = πr²h and substituted the values to find out the Volume of one Cylindrical pillar.

• Now, we have find out the Volume of 14 Cylindrical pillars by multiplying 14 and the Volume of one Cylindrical pillar which is 8.80/7 .

• Therefore, the amount of Concrete mixture to build 14 pillars is 17.6 m³.

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$\pink\bigstar{ \underline { \underline { \bf{↬ \purple{ ExpLore \: MoRe \: ForMuLa}↫}}}} \green \bigstar$

• $\small \sf \: Volume \: of \: a \: Cuboid \large\leadsto \small \boxed{ \bf l \times b \times h}$

• $\small \sf \: Volume \: of \: a \: Cube \large\leadsto \small \boxed{ \bf {a}^{3} }$

• $\small \sf \: Volume \: of \: a \: Cylinder \large\leadsto \small \boxed{ \bf \pi {r}^{2}h }$

• $\small \sf \: Volume \: of \: a \:Cone\large\leadsto \small \boxed{ \bf \frac{1}{3}\pi r {}^{2} h }$

• $\small \sf \: Volume \: of \: a \: Sphere \large\leadsto \small \boxed{ \bf \frac{4}{3} \pi r {}^{3} }$

• $\small \sf \: Volume \: of \: a \: Hemisphere \large\leadsto \small \boxed{ \bf \frac{2}{3}\pi {r}^{3} }$

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