Question

The pillars of a temple are cylindrical shaped. if each pillar has a circular base of radius 30 cm and height 10 m, how much concrete mixture would be required to build 14 such pillars?​

Answer 1

Given:-

• Pillars of a temple are cylindrical shaped
• Radius of base of each pillar = 30
• Height of each pillar = 10 m

To Find:-

• How much concrete mixture would be required to build 14 such pillars.

Solution:-

We know,

To build a pillar we require the amount of concrete required. Hence we need to find volume of the pillar here.

We already have:-

• $\bf{\green{Radius\:of\:base = 30\:cm}}$
• $\bf{\red{Height = 10\:m = 1000\:cm}[\because\:1\:m = 100\:cm]}$

We know,

• $\dag\boxed{\underline{\pink{\bf{Volume\:of\:Cylinder = \pi r^2h\:sq.units}}}}$

Putting all the values, we get:-

$\sf{Volume\:of\:each\:pillar = \dfrac{22}{7}\times (30)^2\times 1000}$

$\sf{Volume\:of\:1\:pillar = \dfrac{22000\times 900}{7}}$

$=\sf{Volume\:of\:1\:pillar = \dfrac{19800000}{7}}$

$\dag{\boxed{\underline{\bf{\therefore\:The\:Volume\:of\:one\:pillar\:is\:\dfrac{19800000}{7}cm^3}}}}$

Now,

$\sf{\because\:Volume\:of\:1\:pillar = \dfrac{19800000}{7}\:cm^3}$

$\sf{\therefore\:Volume\:of\:14\:pillars = 14\times \dfrac{19800000}{7}}$

$= \sf{Volume\:of\:14\:pillars = 2\times19800000 = 39600000\:cm^3}$

$\boxed{\underline{\blue{\bf{\therefore\:The\:required\:Concrete\:mixture\:is\:14\:\:pillars\:is\:3960000\:cm^3\:or\:39.6\:m^3}}}}$

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Answer 2

Answer:

$\large \underline{\sf\pmb{Given}}$

• ➠ Radius of the base of a cylinder = 30 cm
• ➠ Height of Cylinder = 10 m

$\large \underline{{ \sf \pmb{To Find}}}$

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

$\large\underline{\sf \pmb{Using \: Formula }}$

$\circ\underline{ \boxed{ \sf{Volume \: of \: Cylinder \: Piller = {\pi} {r}^{2}h }}}$

$\large \underline{ \sf \pmb{Solution}}$

$\bigstar \: \underline\frak{Firstly \: Converting \: Height \: (30cm) \: into \: m}$

As we know that

$: \implies \sf{1 \: cm = \dfrac{1}{100} \: m}$

So,

$: \implies \sf{30 \: c m = \bigg( \dfrac{30}{100} \bigg)m}$

$: \implies \bf \red{0.3 \: cm}$

$\bigstar \: \underline\frak{Now,Finding \: the \: volume \: of \: a \: pillar}$

${ : \implies \sf{Volume \: of \: Cylinder \: Pillar = {\pi} {r}^{2}h }}$

• Substituting the values

${ : \implies\sf{Volume_{(cylinder \: pillar)}} = \dfrac{22}{7} \times {0.3}^{2} \times 10}$

${ : \implies\sf{Volume_{(cylinder \: pillar)}} = \dfrac{22}{7} \times (0.3 \times 0.3) \times 10}$

${ : \implies\sf{Volume_{(cylinder \: pillar)}} = \dfrac{22}{7} \times 0.09\times 10}$

${ : \implies\sf{Volume_{(cylinder \: pillar)}} = \dfrac{22}{7} \times 0.9}$

${ : \implies\bf {\red{Volume_{(cylinder \: pillar)} = \dfrac{19.8}{7} }}}$

$\circ \underline{ \boxed {\sf \purple{Volume \: of \: a \: Cylinder \: Piller \: is \: 19.8/7 m³}}}$

$\bigstar \: \underline\frak{Now,Finding \: the \: volume \: of \: 14\: pillers.}$

${: \implies\sf{Volume \: of \: 14 \: Piller = 14 \times Volume \: of \: a \: pillar}}$

• Substituting the values

${: \implies\sf{Volume= 14 \times \dfrac{19.8}{7} }}$

${: \implies\sf{Volume= \cancel{14} \times \dfrac{19.8}{ \cancel{7} }}}$

${: \implies\sf{Volume= 2 \times 19.8} \: {m}^{3} }$

${: \implies\bf \red{Volume=39.6 \: {cm}^{3} } }$

$\circ\underline{\boxed {\sf \purple{Volume \: of \: 14 \: pillar \: is \: 39.6 \: {m}^{3}}}}$

• ➠ Henceforth,14 pillars would need 39.6 m³ of concrete mixture.