Question

A cylindrical pipe has an outer diameter of 3 m and an inner diameter of 2 m.Its length is 12 m.It has to be painted on ghe outer and inner surfaces.If the rate of painting is rs 7 per sq. m,find the cost of painting the pipe

Answer 1

Answer :-

• Total Cost of Painting the Pipe = 1319.92 Rs

Given :-

• Inner Diameter of Pipe = 2 m
• Outer Diameter of Pipe = 3 m
• Length (Here Height) of Pipe = 12 m
• Rate of Painting per m² = 7 Rs

To Find :-

• Total Cost of Painting the Pipe = ?

Explanation :-

In order to Find the Total, First need to find the Inner Radius and Outer Radius of Pipe.

$\pink { \boxed { \bf \bigstar \: Radius = \dfrac{Diameter}{2} \: \bigstar }}$

$\rm \odot \: Inner \: Radius \: (r) = \dfrac{2}{2} = \bold{1 \: m}$

$\rm \odot \: Outer \: Radius \: (R)= \dfrac{3}{2} = \bold{1.5 \: m}$

_____________________

Now, We will Find the Inner CSA and Outer CSA of Pipe.

$\green { \boxed { \bf \bigstar \: CSA \: of \: Cylinder = 2 \pi rh \: \bigstar }}$

$\bf 1. \: Inner \: CSA = 2 \pi rh$

$\rm : \: \longrightarrow 2 \times \dfrac{22}{7} \times 1 \times 12$

$\rm : \: \longrightarrow \dfrac{44}{7} \times 12$

$\rm : \: \longrightarrow \dfrac{528}{7}$

$\purple { \bf : \: \longrightarrow 75.42 \: m^2 } \qquad \bold{[Approx.]}$

$\bf 2. \: Outer \: CSA = 2 \pi Rh$

$\rm : \: \longrightarrow 2 \times \dfrac{22}{7} \times 1.5 \times 12$

$\rm : \: \longrightarrow \dfrac{44}{7} \times 18$

$\rm : \: \longrightarrow \dfrac{792}{7}$

$\purple { \bf : \: \longrightarrow 113.14 \: m^2 } \qquad \bold{[Approx.]}$

_____________________

Now, we will Find the Total Area that will be painted.

$\orange { \boxed { \bf \bigstar \: Total \: Area \: for \: Painting = Inner \: CSA + Outer \: CSA \: \bigstar }}$

$\purple { \bf : \: \longrightarrow 188.56 \: m^2 }$

_____________________

Now, we will Find the Cost of Painting.

$\rm : \: \longrightarrow Cost \: of \: Painting \: 1 \: m^2 = \bold{7 \: R_S}$

$\rm : \: \longrightarrow Cost \: of \: Painting \: 188.56 \: m^2$

        $\rm = (188.56 \times 7) \: R_S$

       $\red { \underline { \boxed { \bf = 1319.92 \: R_S }}}$

Hence, the Total Cost Painting the Inner and Outer surfaces of the Pipe is 1319.92 Rs.

Answer 2

Answer:

Rs. 1320...

Step-by-step explanation:

this the correct answer