Question

In a building there are 25 cylindrical pylars . The radius of each pillar is 50 cm and height 5m. Find the cost of painting the curved surface area of the pillars at 70 rs per sq m​

Answer 1

$\underbrace{\underline{\bigstar~\bf Required ~ Answer :-}}$

» In this question, we would first find the Curved Surface Area (CSA) of a single pillar using the given radius and the height .

» Since the rate of painting is given in per m² so, we would change cm into m (for radius).

» We would multiply the CSA of a pillar to 25 so as to get the surface area of 25 pillars.

» The would multiply the area to the rate so as to get the final cost of painting.

◆ Finding CSA of one pillar :

We have :

• Height = 5 m
• Radius = 50 cm = 0.5 m

We know :

$\odot\;\boxed{\sf CSA_{\:cylinder}=2\pi r h}$

So,

$\displaystyle \colon \longrightarrow \sf \: csa _{ \: one \: pillar} = 2 \times \frac{22}{7} \times 0.5 \times 5 \: {m}^{2} \\ \\ \colon \dashrightarrow \boxed{ \bf { { \frak{csa _{ \: one \: pillar} = \pink{\bf \frac{110}{7} \: {m}^{2} }}}}}$

◆ Finding CSA of 25 pillars :

$\colon \longrightarrow \sf \: csa _{ \: 25 \: pillars} = 25 \times csa _{ \: \: one \: pillar} \\ \\ \displaystyle\colon \longrightarrow \sf \: csa _{ \: 25 \: pillars} = 25 \times \dfrac{110}{7} \: {m}^{2} \\ \\ \colon \dashrightarrow \boxed{ \frak{csa _{ \: 25 \: pillars} = \pink{ \bf \frac{2750}{7} \: {m}^{2} }}}$

◆ Finding the cost of painting :

We have :

• CSA of 25 pillars = $\dfrac{2750}{7}$ m²

• Rate of painting = 70 Rs per m²

We know :

$\odot\;\boxed{\sf Cost = Rate \times Area}$

So,

$\displaystyle \colon \implies \sf \: cost _{ \: painting} = \cancel{ 70 }\times \frac{2750}{ \cancel7} \: rs \\ \\ \colon \implies \sf \: cost _{ \: painting} = 10 \times 2750 \: rs \\ \\ \colon \dashrightarrow \underline{ \boxed{ \frak{ \purple{cost _{ \: painting} = \green{\bf 27500 \: rs}}}}}$

$\therefore\:\underline{\sf The\:cost\:of\:painting\:the\:pillars\:would\:be\:\bf{\red{27500}\:Rs}.}$

_____________________________

Answer 2

${ \large{ \underline{ \pmb{ \frak{Given \: that : }}}}}$

★ In a building there are 25 cylindrical pylars .

★ The radius of each pillar is 50 cm and height 5m

★ The cost to paint the Curved surface area of the pillars is at the rate rs. 70 per m²

${ \large{ \underline{ \pmb{ \frak{ To \: find: }}}}}$

★ The Cost of fencing the 25 cylindrical pillars

${ \large{ \underline{ \pmb{ \frak{ Understanding\:the \: concept : }}}}}$

☀️Concept : Here, we have been given that the building has 25 cylindrical pillars and the thier radius is 50cm as that the hieght is 5m each. And the cost of painting them is at 70 rs. per meter

❍Now, So, First we have to find the curved surface area of the 25 pillars and then we should find the cost to painting them.

${ \large{ \underline{ \pmb{ \frak{ Using \: the \: formulae : }}}}}$

★ Formula to find the curved surface area of a right circular cylinder is 2πrh( according to the given measurements),

${ \large{ \underline{ \pmb{ \frak{ Using\:the \: concept : }}}}}$

~Now, We have to use the above mentioned formula and then substitute the values of radius , hieght

Note : before substituting we have to check weather our measurements are in the same units

~here :

Radius = 50cm

hieght = 5m

~As they are different units let's convert the radius from cm to m

${ \underline{ \frak{As \: we \: know \: that}}}$

★ 1m = 100cm

★ 0.5m = 50cm

↬ So, the radius of the cylinder is 0.5m

${ \large{ \underline{ \pmb{ \frak{Solution : }}}}}$

★Cost to paint 25 cylinders = rs 25700

${ \large{ \underline{ \pmb{ \frak{Full \: solution : }}}}}$

~ Firstly let's find curved surface area of 1 cylinder.

let's substitute the values now to find it..!

✪ Curved surface area of a cylinder = 2πrh

$\longrightarrow \tt \: c.s.a \: = 2\pi \: rh \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \\ \longrightarrow \tt \: c.s.a = 2 \times \frac{22}{7} \times 0.5 \times 5 \\ \\ \\ \longrightarrow \tt \: c.s.a = \frac{110}{7} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:$

• There fore curved surface area of 1 cylinder = 110/7m²

~Now, let's find the curved surface area of 25 cylinders

✪ Curved surface area of 25 cylinders = c.s.a of 1 cylinder times 25

➠ 25 × 110/7

➠ 2570/7m²

➽Now let's find the cost to paint them,As we know that the cost to paint is 70rs. per m² let's multiply it with 70 per sq.units

➠ 70 × 2570 /7

➠ 2570 × 10

➠rs.25700

Hence:

• The cost to paint the cylinders in total is rupees 25700

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Diagram:

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