# 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

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?​

1. ## Given:–

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

### ToFind:–

• 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.

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

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

• ➠ 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.