Question

Int a building there are 22 cylindrical pillars . The radius of each pillar is 28cm and height is 4m . Find the total cost of painting the curved surface are of all pillars at the rate of 5rs per sq.m

Answer 1

${\large{\sf{\pmb{\underline{Given \; that...}}}}}$

• Total pillars = 22
• Shape of pillars = Cylindrical
• Radius = 28 cm
• Height = 4 metres

${\large{\sf{\pmb{\underline{To \; find...}}}}}$

• The total cost of painting a curved surface area of all the pillars at a rate of Rupees 5 per square metre.

${\large{\sf{\pmb{\underline{Solution...}}}}}$

• The total cost of painting a curved surface area of all the pillars at a rate of Rupees 5 per square metre = 773.696 Rupees

${\large{\sf{\pmb{\underline{Using \; concepts...}}}}}$

• Formula to convert centimetres into metres.

• Formula to find curved surface area of a cylinder.

• Formula to find curved surface area of 24 cylinder's (pillars)

• Formula to find the total cost of painting a curved surface area of all the pillars at a rate of Rupees 5 per square metre (according to the question.)

${\large{\sf{\pmb{\underline{Using \; formulas...}}}}}$

${\small{\underline{\boxed{\sf{1 \: m \: = 100 \: cm}}}}}$

${\pmb{\sf{\qquad \qquad \qquad \qquad \qquad \ddag \: \: \: Henceforth,}}}$

${\small{\underline{\boxed{\sf{\circ \: \: 1 \: cm \: = 1/100 \: m}}}}}$

${\small{\underline{\boxed{\sf{\circ \: \: CSA \: of \: cylinder \: = 2 \pi r h}}}}}$

${\small{\underline{\boxed{\sf{\circ \: \: CSA \: of \: \: 24 \: cylinders \: = 22 \times CSA \: of \: a \: Cylinder}}}}}$

${\small{\underline{\boxed{\sf{\circ \: \: CSA \times Given \: rate \: i.e., \: 5 \: Rupees}}}}}$

${\large{\sf{\pmb{\underline{Where,}}}}}$

• CSA - curved surface area.
• r denotes radius
• h denotes height
• m denotes metres
• cm denotes centimetres
• π is pronounced as pi
• Value of π = 22/7 or 3.14

${\large{\sf{\pmb{\underline{Full \; Solution \: with \: procedure...}}}}}$

~ Firstly as it's given that we have radius and height in different units as cm and metres respectively. So firstly let us convert onf if them into another. Let's convert cm into m. But if you want to convert m into cm then you can but it's better to change m into cm. Let's convert them by using formula!

${\small{\underline{\boxed{\sf{\circ \: \: 1 \: cm \: = 1/100 \: m}}}}}$

${\sf{:\implies 1 \: cm \: = 1/100 \: m}}$

${\pmb{\sf{\qquad \qquad \qquad \qquad \qquad 28 \: cm \: are \: given \: here}}}$

${\sf{:\implies 28/100 m}}$

${\sf{:\implies 0.28 \: m}}$

${\underline{\frak{Henceforth, \: 0.28 \: m \: is \: the \: radius \: of \: pillars}}}$

New Diagram is given below according to the new converted radius -

$\setlength{\unitlength}{1mm}\begin{picture}(5,5)\thicklines\multiput(-0.5,-1)(26,0){2}{\line(0,1){40}}\multiput(12.5,-1)(0,3.2){13}{\line(0,1){1.6}}\multiput(12.5,-1)(0,40){2}{\multiput(0,0)(2,0){7}{\line(1,0){1}}}\multiput(0,0)(0,40){2}{\qbezier(1,0)(12,3)(24,0)\qbezier(1,0)(-2,-1)(1,-2)\qbezier(24,0)(27,-1)(24,-2)\qbezier(1,-2)(12,-5)(24,-2)}\multiput(18,2)(0,32){2}{\sf{0.28 \: m}}\put(9,17.5){\sf{4 \: m}}\end{picture}$

~ Now let's find the curved surface area of a cylindrical pillar by using the formula to find curved surface area of cylinder. We just have to put the values according to the formula! Let's solve!

${\small{\underline{\boxed{\sf{\circ \: \: CSA \: of \: cylinder \: = 2 \pi r h}}}}}$

${\sf{:\implies CSA \: of \: cylinder \: = 2 \pi r h}}$

${\sf{:\implies CSA \: of \: cylinder \: = 2(3.14)(0.28)(4)}}$

${\sf{:\implies CSA \: of \: cylinder \: = 2 \times 3.14 \times 0.28 \times 4}}$

${\sf{:\implies CSA \: of \: cylinder \: = 6.28 \times 0.28 \times 4}}$

${\sf{:\implies CSA \: of \: cylinder \: = 1.7584 \times 4}}$

${\sf{:\implies CSA \: of \: cylinder \: = 7.0336 \: m^{2}}}$

${\sf{:\implies CSA \: of \: cylindrical \: pilar \: = 7.0336 \: m^{2}}}$

${\underline{\frak{Henceforth, \: 7.0336 \: m^{2} \: is \: the \: CSA \: of \: cylindrical \: pillar}}}$

~ Now let's find the CSA of 22 cylindrical pillars, we just have to multiply CSA of a cylindrical pillar that is 7.0336 m² by total number of pillars that is 22. Let's do it!

${\small{\underline{\boxed{\sf{\circ \: \: CSA \: of \: \: 24 \: cylinders \: = 22 \times CSA \: of \: a \: Cylinder}}}}}$

${\sf{:\implies CSA \: = 22 \times 7.0336}}$

${\sf{:\implies CSA \: = 154.7392 \: m^{2}}}$

${\underline{\frak{Henceforth, \: 154.7392 \: m^{2} \: is \: the \: CSA \: of \: 22 \: cylindrical \: pillars}}}$

~ Now let's find the total cost of painting a curved surface area of all the pillars at a rate of Rupees 5 per square metre. Just have to put the values according to the formula means have to multiply 5 by 154.7392. Let's do it!

${\small{\underline{\boxed{\sf{\circ \: \: CSA \times Given \: rate \: i.e., \: 5 \: Rupees}}}}}$

${\sf{:\implies Cost \: = 154.7392 \times 5}}$

${\sf{:\implies Cost \: = 773.696 \: Rupees}}$

${\underline{\frak{Henceforth, \: 773.696 \: Rupees \: is \: the\: cost}}}$