Question

In a building there are 24 cylindrical pillars. The radius of each pillar is 280 cm and height is 7 m. Find the total cost of painting the curved surface area of all pillars at the rate of Rs 8 per m2​

Answer 1

★ Answer ★

${ \bold { \underline{\large\pink{Correct \: Question : - }}}} \:$

In a building there are 24 cylindrical pillars. The radius of each pillar is 280 cm and height is 7m. Find the total cost of painting the curved surface area of all pillars at the rate of Rs.8 per m².

${ \bold { \underline{\large\pink{Given : - }}}} \:$

★ Radius of pillar = 280 cm

Converting in m.

= 2.8m

★ Height of pillar = 7m

⠀

${ \bold { \underline{\large\pink{To \: Find : - }}}} \:$

★ Total cost of painting the curved surface area of all pillars at the rate of Rs.8 per m².

⠀

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

Step by step explanation:-

As we all know that the pillar is in cylindrical shape.

So, Now applying the Curved surface area of cylinder

Curved surface area of cylinder = 2πrh

★ Using Formula

${\boxed{\sf{\purple{C.S.A\: of\: a\: cylinder = 2\pi rh}}}}$

By Substituting the values in the above formula, we get

⠀

C.S.A of a pillar = $2 × \sf{\dfrac{22}{7} × 2.8 × 7}$

$\longmapsto\tt{CSA =2\times\dfrac{22}{{\cancel{7}}}\times{2.8}\times{{\cancel{7}}}}$

⠀⠀⠀⠀⠀⠀⠀⠀⠀ $\sf{= 123.2m^2}$

C.S.A of 24 such pillar = $\sf{123.2× 24}$

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀ $\sf{= 2596.6m^2}$

Cost of painting an area of 1m² = $\sf{Rs.8}$

Therefore,

Cost of painting $\sf{2956.6m^2}$ = $\sf{2956.6 × 8}$

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀$\sf{= Rs.23654.4}$

Hence,

➤ Cost of painting 24 pillars ↬ 23654.4Rs.

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Answer 2

Correct Question-:

• In a building there are 24 cylindrical pillars. The radius of each pillar is 280 cm and height is 7 m. Find the total cost of painting the curved surface area of all pillars at the rate of Rs 8 per m²

AnswEr -:

$\boxed{\sf{\purple{The\:cost\:of\:painting \:of\:24\:cylindrical \:pillars \:is\: Rs. 23654.4 }}}$

Explanation-:

Given ,

• In a building there are 24 cylindrical pillars.
• The radius of each pillar is 280 cm .
• The height of pillars are 7 m .
• The rate of painting is Rs. 8 per m² .

To Find ,

• The total cost of painting the curved surface area of all pillars .

Solution -:

☆ Using Formula-:

$\boxed{\sf{\pink{ The \:C.S.A\: of\: cylindrical\: pillars\: -: 2\: π\: r\: h}}}$

Here,

• R = Radius = 280 cm
• H = Height
• π = $\sf{\frac{22}{7}}$ or 3.14

▪︎ As ,We know that ,

$\boxed{\sf{\red{1m = 100 cm}}}$

Then ,

• Radius -: $\sf{\frac{280}{100}}$ = 2.8 m

$\sf{\rightarrow{\red{2 \times \frac {22}{7} \times 2.8 \times 7}}}$

$\sf{\rightarrow{\red{2 \times \ 22 \times 2.8 }}}$

$\sf{\rightarrow{\red{44 \times 2.8 }}}$

$\sf{\rightarrow{\red{ 123.2 m² }}}$

Therefore,

$\boxed{\sf{\rightarrow{\red{ C.S.A\: = 123.2 m² }}}}$

☆ C.S.A of 24 pillars -:

$\sf{\rightarrow{\blue{123.2 \times 24 }}}$

$\boxed{\sf{\rightarrow{\blue{ 2596.6 m² }}}}$

☆ Cost of painting at Rs. 8 per m ² -:

$\sf{\rightarrow{\red {2596.6 \times 8 }}}$

$\boxed{\sf{\rightarrow{\blue {Rs. 23654.4 }}}}$

Hence ,

$\boxed{\sf{\purple{The\:cost\:of\:painting \:of\:24\:cylindrical \:pillars \:is\: Rs. 23654.4 }}}$

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