Question

$\huge \bf Question$

● The pillars of a temple are cylindrically shaped. If each pillar has a circular base of radius 20cm and height 10m, how much concrete mixture would be required to build 14 such pillars ?

▪︎Note:-

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Answer 1

★ Correct Question :-

The pillars of a temple are cylindrically shaped. If each pillar has a circular base of radius 20cm and height 10m, how much concrete mixture would be required to build 14 such pillars ?

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★ Concept ::

Here the concept of Volume of Cylinder has been used. We see that the pillars are Cylindrical in shape and each pillar is made up of concrete mixture. We have to find the amount of concrete mixture. We are given the dimensions of the pillar. If we find the volume of the pillar, then we will get volume of concrete used in one pillar and thus we can find for 14 such pillars.

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★ Formula Used :-

$\;\boxed{\sf{\pink{Volume\;of\;Cylinder\;=\;\bf{\pi r^{2}h}}}}$

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★ Solution :-

» Radius of each pillar = r = 20 cm

» Height of the pillar = H = 10 cm

» Number of pillars = 14

» Shape of solid that is pillar = Cylinder

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~ For the Volume of each pillar ::

We know that,

$\;\sf{\rightarrow\;\;Volume\;of\;Cylinder\;=\;\bf{\pi r^{2}h}}$

By applying values, we get

$\;\sf{\rightarrow\;\;Volume\;of\;Pillar\;=\;\bf{\pi\:\times\:(20)^{2}\:\times\:10}}$

$\;\sf{\rightarrow\;\;Volume\;of\;Pillar\;=\;\bf{\pi\:\times\:20\:\times\:20\:\times\:10}}$

$\;\sf{\rightarrow\;\;Volume\;of\;Pillar\;=\;\bf{\pi\:\times\:400\:\times\:10}}$

$\;\sf{\rightarrow\;\;Volume\;of\;Pillar\;=\;\bf{\pi\:\times\:4000}}$

$\;\sf{\rightarrow\;\;Volume\;of\;Pillar\;=\;\bf{\red{4000\pi\;\:cm^{3}}}}$

This is the Volume of Concrete used in on Pillar.

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~ For amount of concrete used in 14 pillars ::

We already got the value of volume of one pillar. So, volume of 14 pillars will be

✒ Volume of 14 such pillars = 14 × Volume of one pillar

$\;\bf{\Longrightarrow\;\;Volume\;of\;14\;pillars\;=\;14\:\times\;4000\pi}$

By applying the value of π as 22/7 , we get

$\;\bf{\Longrightarrow\;\;Volume\;of\;14\;pillars\;=\;14\:\times\;4000\:\times\:\dfrac{22}{7}}$

$\;\bf{\Longrightarrow\;\;Volume\;of\;14\;pillars\;=\;2\:\times\;4000\:\times\:22}$

$\;\bf{\Longrightarrow\;\;Volume\;of\;14\;pillars\;=\;176000\;\;cm^{2}}$

Thus this the required answer, which shows the amount of concrete in 14 pillars.

$\;\underline{\boxed{\tt{Total\;\:Amount\;\:of\;\:concrete\;\:mixture\;=\;\bf{\purple{176000\;\;cm^{2}}}}}}$

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★ More to know :-

$\;\tt{\leadsto\;\;TSA\;of\;Cylinder\;=\;2\pi rH\;+\;\pi r^{2}}$

Answer 2

Height of cylinder = h = 10m

Radius = r = 20cm

= 20 × 1/100m = 2/10m

Volume of concrete in one cylindrical pillar = π²h

= 22/7 × 2/10 × 2/10 × 10m³

= 88/70m³

∴Volume of concrete in 1 cylindrical pillar = 88/70m³

So, volume of concrete in 14 pillars = 14 × 88/70m³

= 17.6m³