Question

in m
A cylindrical pillar is 50 cm in diameter and 3.5 m in height. Find the cost of painting
the curved surface of the pillar at the rate of 12.50 per m².
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Answer 1

★ Answer ★

The cost of painting the pillar = 68.75 Rs.

Step by step explanation:-

★ Given :-

• Diameter of the Pillar - 50 cm or 0.5 m
• Height of the Pillar - 3.5 m or 350 cm
• The cost of painting per m² is Rs. 12.50

★ Have to Find :-

• Find the cost of painting the pillar.

★ Solution :-

$\pink{Formula \: Information :-}$

CSA of a Cylinder :-

$\bf{\underline{CSA = 2\pi rh}}$

Where :-

r = Radius of the cylinder

h = Height of the cylinder

★ According to the Question :

Have to find the radius of the base of the cylinder first.

We Know that ,

$\Rightarrow \bf{Radius = \dfrac{Diameter}{2}}$

Given , Diameter = $\purple{0.5 m}$

Putting the value in the diameter , we get :

$\implies \bf{Radius = \dfrac{Diameter}{2}} \\ \\ \implies \bf{Radius = \dfrac{0.5}{2}} \\ \\ \implies \bf{Radius = 0.25 m}$

Hence the Radius of the Cylinder is 0.25 m.

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

By Substituting the values in the above formula, we get

$\longmapsto\tt{CSA =2\times\dfrac{22}{{\cancel{7}}}\times{0.25}\times{{\cancel{3.5}}}}$

$\implies \bf{CSA = 2 \times 22\times 0.25\times 0.5} \\ \\ \\ \implies \bf{CSA = 44 \times 0.125 } \\ \\ \\ \therefore \purple{\bf{CSA = 5.5 m^{2}}}$

Now, from given cost for 1 pillar ↬ 12.50

Hence,

➤ Cost of painting pillar → CSA × Per metre cost.

↬ 5.5 × 12.50 = 68.75 Rs.

★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★

Answer 2

★ Given Question :-

A cylindrical pillar is 50 cm in diameter and 3.5 m in height. Find the cost of painting the curved surface of the pillar at the rate of 12.50 per m².

Let's do it !!

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★ Formula Used :-

$\begin{gathered}\\\;\boxed{\sf{\pink{Curved \: Surface \: Area\;=\;\bf{2\pi rh}}}}\end{gathered}$

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★ Solution :-

Given,

» Diameter of cylindrical pillar = 50 cm

» Height of a cylindrical pillar = 3.5 m

To find ,

» Cost of painting the curved surface of the pillar at the rate of = 12.50 per m²

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~ It is given in the question that the shape of the pillars is cylindrical in shape

We know that,

$\begin{gathered}\\\;\sf{Curved \: Surface \: Area\;=\;\bf{2\pi rh}}\end{gathered}$

Now we know ,

• Value of π ( pi ) = 22/7

• Value of r ( radius )= Half of diameter = 50/2 = 25 cm [ now we need to convert it into m ] = 25/100 = 0.25 m

• Value of h ( height ) = 3.5 m

Let's put the value

$\begin{gathered}\\\;\sf{:\rightarrow\;\;Curved \: Surface \: Area\;=\;\bf \color{lime}{2\pi rh}}\end{gathered}$

After putting value ,

$\begin{gathered}\\\;\sf{:\rightarrow\;\;Curved \: Surface \: Area\;=\;\bf \color{lime}{2 \times \frac{22}{7} \times 0.25 \times 3.5 }}\end{gathered}$

$\begin{gathered}\\\;\sf{:\rightarrow\;\;Curved \: Surface \: Area\;=\;\bf {44 \times 0.125 }}\end{gathered}$

$\begin{gathered}\\\;\sf{:\Longrightarrow\;\;Curved \: Surface \: Area\;=\;\bf \color{cyan}{5.5 {m}^{2} }}\end{gathered}$

Now , it is given to us that

Cost of painting per m² = 12.50 rs

Therefore , Cost of painting 5.5 m² = 12.50 × 5.5 = Rs 68.75

$\begin{gathered}\\\;\underline{\boxed{\tt{Cost\;\:of\;\: Painting\;=\;\bf{\green{Rs \: 68.75}}}}}\end{gathered}$