Question

The pillars of a temple are cylindrical shaped. if 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

Given :

The pillars of a temple are cylindrical shaped. if each pillar has a circular base of radius 20 cm and height 10 m

To Find :-

Concrete mixture would be required to build 14 such pillars

Solution :-

We know that

Volume of cylinder = πr²h

Volume = π × (20)² × 10

Volume = 314/100 × 400 × 10

Volume = 314 × 4 × 10

Volume = 12560 cm³

Now

Amount of concrete required = 14 × Volume

Amount of concrete required = 14 × 12560

Amount of concrete required = 1,75,840 cm³

[tex][/tex]

Answer 2

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

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

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

$\begin{gathered} \\ \end{gathered}$

$\begin{gathered} \\ \end{gathered}$

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

$\begin{gathered}✪ \sf Volume \: of \: one \: cylindrical \: pillar \: \: \: \: \: \: \: \: \: \\ ✪ \sf Volume \: of \: 14 \: cylindrical \: pillars \: \: \: \: \: \: \: \: \: \\ ✪ \sf Concrete \: mixture \: to \: build \: 14 \: pillars \: \end{gathered}$

$\begin{gathered} \\ \end{gathered}$

$\begin{gathered} \\ \end{gathered}$

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

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

$\begin{gathered} \\ \end{gathered}$

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

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

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

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

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

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

$\begin{gathered} \\ \\ \end{gathered}$

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

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

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

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

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

$\begin{gathered} \\ \end{gathered}$

$\begin{gathered} \\ \end{gathered}$

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

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

$\begin{gathered} \\ \end{gathered}$

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

$\begin{gathered} \\ \end{gathered}$

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

$\begin{gathered} \\ \end{gathered}$

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

$\begin{gathered} \\ \end{gathered}$

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

$\begin{gathered} \\ \end{gathered}$

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

$\begin{gathered} \\ \end{gathered}$

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

$\begin{gathered} \\ \end{gathered}$

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

$\begin{gathered} \\ \end{gathered}$

$\begin{gathered} \\ \end{gathered}$