Question

In a building there are 24 cylindrical pillars. The radius of each pillar
is 1 m and height is 7 m. Find the total cost of painting the curved surface area of
all pillars at the rate of 8 per m².​

Answer 1

Given:-

• In a building there are 24 cylindrical pillars.
• Radius of each pillar is 1 m.
• Height of each pillar is 7m.
• Rate of painting is 8 per m².

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To find:-

• Total cost of painting the curved surface area of all pillars.

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Solution:-

★Formula used:-

$\star{\boxed{\sf{\orange{Curved\: surface\: area\: of\: a\: cylinder = 2 \pi rh}}}}$

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$\tt\longmapsto{2 \times \dfrac{22}{7} \times 1 \times 7}$

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$\tt\longmapsto{2 \times 22 \times 1}$

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$\tt\longmapsto{44 \times 1}$

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$\tt\longmapsto{\boxed{\red{44\: m^2}}}$

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Now,

• Curved surface area of 24 pillars.

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$\tt\longmapsto{24 \times 44}$

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$\tt\longmapsto{\boxed{\purple{1056\: m^2}}}$

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Now,

• Cost of painting at the rate of 8 per m².

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$\tt\longmapsto{Rs. (8 \times 1056)}$

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$\tt\longmapsto{Rs. 8448}$

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Hence,

• the total cost of painting is Rs.8448.

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Diagram:-

$\setlength{\unitlength}{1mm}\begin{picture}(5,5)\thicklines\multiput(-0.5,-1)(26,0){2}{\line(0,1){40}}\multiput(12.5,-1)(0,3.2){13}{\line(0,1){1.6}}\multiput(12.5,-1)(0,40){2}{\multiput(0,0)(2,0){7}{\line(1,0){1}}}\multiput(0,0)(0,40){2}{\qbezier(1,0)(12,3)(24,0)\qbezier(1,0)(-2,-1)(1,-2)\qbezier(24,0)(27,-1)(24,-2)\qbezier(1,-2)(12,-5)(24,-2)}\multiput(18,2)(0,32){2}{\sf{1m}}\put(9,17.5){\sf{7m}}\end{picture}$

Answer 2

Given

• There are 24 cylindrical pillars.
• Radius of cylindrical pillar = 1m
• Height of cylindrical pillar = 7m
• Rate of painting = ₹8 per m²

⠀

To find

• Total cost of painting the curved surface area of all 24 pillars.

⠀

Solution

• Firstly, we have to find the curved surface area of one pillar.

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⠀⠀⠀⠀⠀⠀⠀$\setlength{\unitlength}{1mm}\begin{picture}(5,5)\thicklines\multiput(-0.5,-1)(26,0){2}{\line(0,1){40}}\multiput(12.5,-1)(0,3.2){13}{\line(0,1){1.6}}\multiput(12.5,-1)(0,40){2}{\multiput(0,0)(2,0){7}{\line(1,0){1}}}\multiput(0,0)(0,40){2}{\qbezier(1,0)(12,3)(24,0)\qbezier(1,0)(-2,-1)(1,-2)\qbezier(24,0)(27,-1)(24,-2)\qbezier(1,-2)(12,-5)(24,-2)}\multiput(18,2)(0,32){2}{\sf{1 m}}\put(9,17.5){\sf{7 m}}\end{picture}$

⠀⠀⠀⠀⠀⠀⠀⠀⠀Diagram

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$\large{\underline{\boxed{\bf{CSA_{(Cylinder)} = 2 \pi rh}}}}$

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$\: \: \: \: \: \: \: \: \: \rm\underline{\blue{Finding\: CSA\: of\: one\: pillar}}$

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$\tt\longrightarrow{CSA = 2 \times \dfrac{22}{\cancel{7}} \times 1 \times \cancel{7}}$

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$\tt{\longrightarrow{CSA = 2 \times 22}}$

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$\bf{\longrightarrow{CSA = 44m^2}}$

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$\: \: \: \: \: \: \: \: \: \rm\underline{\blue{Now,\: CSA\: of\: 24\: pillars }}$

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$\tt{\longrightarrow{24 \times (CSA\: of\: one\: pillars)}}$

$\tt{\longrightarrow{24 \times 44}}$

$\bf{\longrightarrow{1056m^2}}$

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★ Cost of painting the pillars.

$\tt{\longrightarrow{}}$₹(Rate of painting × CSA of 24 pillars)

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$\tt{\longrightarrow{Rs(8 \times 1056)}}$

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$\bf{\longrightarrow{Rs.8,448}}$

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Hence,

• The total cost of painting the 24 pillars is ₹8,448.

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