Question

In a temple there are 20 cylindrical pillars .The radius of each pillar is 21cm and height is 5m.Find the total cost of painting the curved surface area of the 20 pillars at the rate of Rs 120 per m².​

Answer 1

$\begin{gathered}\begin{gathered}\bf \: Given \:  - \begin{cases} &\sf{number \: of \: cylindrical \: pillars = 20} \\ &\sf{radius \: of \: pillar \: = 21 \: cm}\\ &\sf{height \: of \: pillar = 5 \: m}\\ &\sf{Cost \: of \: {1 \: m}^{2} = Rs \: 120} \end{cases}\end{gathered}\end{gathered}$

$\begin{gathered}\begin{gathered}\bf \: To\:find - \begin{cases} &\sf{Cost \: of \: plastering \: 20 \: pillars.}  \end{cases}\end{gathered}\end{gathered}$

$\begin{gathered}\Large{\bold{{\underline{Formula \: Used \::}}}} \end{gathered}$

• Curved Surface Area of cylinder is given by

$\rm :\longmapsto\: \large \boxed{ \bf \: CSA_{(Cylinder)} = 2\pi \: rh}$

where,

• r is radius of cylinder

• h is height of cylinder

$\large\underline{\bold{Solution :- }}$

Given that

• Radius of cylindrical pillar, r = 21 cm = 0.21 m

• Height of cylindrical pillar, h = 5 m

So,

• Curved Surface Area of 1 cylindrical pillar is given by

$\rm :\longmapsto\:CSA_{(pillar)} = 2\pi \: rh$

$\rm :\longmapsto\:CSA_{(pillar)} =2 \times \dfrac{22}{7} \times 0.21 \times 5$

$\rm :\longmapsto\:CSA_{(pillar)} =6.6 \: {m}^{2}$

So,

Curved Surface Area of 20 cylindrical pillars is given by

$\rm :\longmapsto\:CSA_{(20 \: pillars)} = \: 20 \times 6.6$

$\rm :\longmapsto\:CSA_{(20 \: pillar)} = \: 132 \: {m}^{2}$

Now,

$\rm :\longmapsto\:Cost \: of \: plastering \: {1 \: m}^{2} = Rs \: 120$

$\rm :\longmapsto\:Cost \: of \: plastering \: {132 \: m}^{2} = Rs \: 120 \times 132$

$\rm :\longmapsto\:Cost \: of \: plastering \: \bf{132 \: m}^{2} = Rs \: 15840$

Hence,

$\bf :\longmapsto\:Cost_{(of \: plastering \: 20 \: pillars)} = \: Rs \: 15840$

Additional Information :-

Perimeter of rectangle = 2(length× breadth)

Diagonal of rectangle = √(length²+breadth²)

Area of square = side²

Perimeter of square = 4× side

Volume of cylinder = πr²h

T.S.A of cylinder = 2πrh + 2πr²

Volume of cone = ⅓ πr²h

C.S.A of cone = πrl

T.S.A of cone = πrl + πr²

Volume of cuboid = l × b × h

C.S.A of cuboid = 2(l + b)h

T.S.A of cuboid = 2(lb + bh + lh)

C.S.A of cube = 4a²

T.S.A of cube = 6a²

Volume of cube = a³

Volume of sphere = 4/3πr³

Surface area of sphere = 4πr²

Volume of hemisphere = ⅔ πr³

C.S.A of hemisphere = 2πr²

T.S.A of hemisphere = 3πr²