Question

A cylindrical vessel open at the top has a base diameter of 21cm and height 14cm. Find the cost of tin plating it's inner part at the rate of Rs 5per 100^2.​

Answer 1

Given:-

• Diameter = 21 cm
• Therefore ,Radius = 21/2 = 10.5 cm
• Height = 14 cm
• Rate of painting = ₹ 5 per 100².

To find :-

• Cost of painting = ?

{First we have to find Curved surface area and Area of Base of the Cylindrical Vessel.}

So, Curved Surface Area = C.S.A:-

$\Large{\boxed{\color{orange}{\mathtt{C.S.A= 2\pi \: rh}}}}</strong><strong>$

$\\ \bold{\mathtt{\leadsto{{C.S.A} = 2 \times \frac{22}{7} \times 10.5 \times 14}}}$

$\mathtt{ \leadsto{C.S.A = 2 \times 22 \times 1.5 \times 14}}$

${\color{purple}{\leadsto}{\mathtt{C.S.A = 924 \: \: {cm}^{2} }}}$

Area of the base of Cylindrical Vessel which is circle :-

$\Large{\boxed{\color{orange}{\mathtt{Area{ \:_{(circle) }}= \pi {r}^{2} }}}}</strong><strong>$

$</strong><strong> </strong><strong>\</strong><strong>\</strong><strong> </strong><strong>{\mathtt{ \leadsto \: Area{ \:_{(circle) }}= \frac{22}{7} \times {(10.5)}^{2} }}$

$</strong><strong> </strong><strong>\</strong><strong>\</strong><strong> </strong><strong>{\mathtt{ \leadsto \: Area{ \:_{(circle) } = \frac{22}{7} \times 110.25}}}$

${\mathtt{ \leadsto \: Area{ \:_{(circle) } =22 \times 15.75 }}}$

$\color{purple}{\mathtt{ \leadsto \: Area{ \:_{(circle) } =346.5 \: \: {cm}^{2} }}}$

Adding the both area :-

$\large \boxed{ \color{orange}{ \mathtt{Area \: \: of \: \: Opened \: \: cylinder = Area{ \:_{(circle) }} + C.S.A}}}$

${ \mathtt{Area \: \: of \: \: Opened \: \: cylinder =346.5 + 924}}$

$\purple{ \mathtt{Area \: \: of \: \: Opened \: \: cylinder =1270.5}}$

Cost of painting the Cylindrical Vessel:-

$</strong><strong> </strong><strong>\large </strong><strong>{</strong><strong>\boxed{\mathtt{\color{orange}</strong><strong>{Cost = Rate × Area }}</strong><strong>}</strong><strong>}</strong><strong>$

$\\ \mathtt{\leadsto{Cost = 5 \times \frac{1270.5}{100} }}$

$\mathtt{\leadsto{Cost = 5 \times 12.705}}$

$\LARGE{ \color{green}{ \boxed{{\mathtt{\implies{Cost = 63.525 \: \: Rs}}}}}}$

Therefore cost of painting is 63.525 Rs .

Answer 2

Answer:

Cost of painting at rate of Rs5 per 100 m² is RS 63.525