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 concr

2 thoughts on “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 concr”

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:-

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

   We know,

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

   Putting all the values, we get:-

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

   [tex]\sf{Volume\:of\:1\:pillar = \dfrac{22000\times 900}{7}}[/tex]

   [tex]=\sf{Volume\:of\:1\:pillar = \dfrac{19800000}{7}}[/tex]

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

   Now,

   [tex]\sf{\because\:Volume\:of\:1\:pillar = \dfrac{19800000}{7}\:cm^3}[/tex]

   [tex]\sf{\therefore\:Volume\:of\:14\:pillars = 14\times \dfrac{19800000}{7}}[/tex]

   [tex] = \sf{Volume\:of\:14\:pillars = 2\times19800000 = 39600000\:cm^3}[/tex]

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

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2. Answer:

   [tex] \large \underline{\sf\pmb{Given}}[/tex]

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

   [tex] \large \underline{{ \sf \pmb{To Find}}}[/tex]

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

   [tex] \large\underline{\sf \pmb{Using \: Formula }}[/tex]

   [tex] \circ\underline{ \boxed{ \sf{Volume \: of \: Cylinder \: Piller = {\pi} {r}^{2}h }}}[/tex]

   [tex] \large \underline{ \sf \pmb{Solution}}[/tex]

   [tex] \bigstar \: \underline\frak{Firstly \: Converting \: Height \: (30cm) \: into \: m}[/tex]

   As we know that

   [tex] : \implies \sf{1 \: cm = \dfrac{1}{100} \: m}[/tex]

   So,

   [tex] : \implies \sf{30 \: c m = \bigg( \dfrac{30}{100} \bigg)m}[/tex]

   [tex] : \implies \bf \red{0.3 \: cm}[/tex]

   [tex] \bigstar \: \underline\frak{Now,Finding \: the \: volume \: of \: a \: pillar}[/tex]

   [tex]{ : \implies \sf{Volume \: of \: Cylinder \: Pillar = {\pi} {r}^{2}h }}[/tex]

   • Substituting the values

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

   [tex]{ : \implies\sf{Volume_{(cylinder \: pillar)}} = \dfrac{22}{7} \times (0.3 \times 0.3) \times 10}[/tex]

   [tex]{ : \implies\sf{Volume_{(cylinder \: pillar)}} = \dfrac{22}{7} \times 0.09\times 10}[/tex]

   [tex]{ : \implies\sf{Volume_{(cylinder \: pillar)}} = \dfrac{22}{7} \times 0.9}[/tex]

   [tex]{ : \implies\bf {\red{Volume_{(cylinder \: pillar)} = \dfrac{19.8}{7} }}}[/tex]

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

   [tex] \bigstar \: \underline\frak{Now,Finding \: the \: volume \: of \: 14\: pillers.}[/tex]

   [tex] {: \implies\sf{Volume \: of \: 14 \: Piller = 14 \times Volume \: of \: a \: pillar}}[/tex]

   • Substituting the values

   [tex]{: \implies\sf{Volume= 14 \times \dfrac{19.8}{7} }}[/tex]

   [tex]{: \implies\sf{Volume= \cancel{14} \times \dfrac{19.8}{ \cancel{7} }}}[/tex]

   [tex]{: \implies\sf{Volume= 2 \times 19.8} \: {m}^{3} } [/tex]

   [tex]{: \implies\bf \red{Volume=39.6 \: {cm}^{3} } }[/tex]

   [tex] \circ\underline{\boxed {\sf \purple{Volume \: of \: 14 \: pillar \: is \: 39.6 \: {m}^{3}}}}[/tex]

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

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