Question

pls ans fast and right

A metal pipe is 77 cm long. The inner diameter of a cross secion is 4 cm and the thickness is

0.2 cm , Find its total surface area.​

Answer 1

Given:

• The length (h) of the hollow metallic cylinder is 77cm
• The inner diameter = 4 cm
• The inner radius (r) = 4/2 = 2 cm
• Also, thickness is 0.2 cm
• So, outer radius (R) = inner radius + thickness
• R = 2 + 0.2 = 2.2 cm

Now,

To find:

The Total Surface Area of the hollow cylinder

• The formula to find the TSA of the hollow cylinder is

= 2π (R + r)(h + R - r) unit sq,

[In which, 'R' is the outer radius, 'r' is the inner radius and 'h' is the height(i.e. length) of the hollow cylinder]

Now putting the given values,

$\bf TSA = 2*\frac{22}{7}(2.2+2)(77+2.2-2)$

$\bf TSA = 2*\frac{22}{7}(4.2)(79.2-2)$

$\bf TSA = 2*\frac{22}{7}(4.2)(77.2)$

$\bf TSA = \frac{14266.56}{7}$

TSA of the hollow metallic cylinder = 2038.08 cm sq.

MORE INFORMATION:

The total surface area of the hollow cylinder

= 2πRh + 2πrh + 2π(R² - r²)

= 2πh(R+h) + 2π(R + r)(R - r)

= 2π(R + r)(h + R - r)

Answer 2

Answer:

Given :-

• A metal pipe is 77 cm long.
• The inner diameter of a cross section is 4 cm and the thickness is 0.2 cm.

To Find :-

• What is the total surface area.

Solution :-

Given :

• Height = 77 cm

$\mapsto$ Inner diameter (r₁) = 4 cm

So, we know that :

$\longmapsto \sf\boxed{\bold{\pink{Radius =\: \dfrac{Diameter}{2}}}}$

Then,

$\implies \sf Inner\: radius =\: \dfrac{\cancel{4}}{\cancel{2}}$

$\implies \sf\bold{\green{Inner\: radius =\: 2\: cm}}$

So, their curved surface area will be :

$\implies \sf C.S.A =\: 2{\pi}r_1h$

$\implies \sf C.S.A =\: 2 \times \dfrac{22}{7} \times 2 \times 77$

$\implies \sf\bold{\blue{C.S.A =\: 968\: {cm}^{2}}}$

• Thickness = 0.2 cm

So, we have to find the outer radius (r₂) ,

$\implies \sf Outer\: radius =\: Thickness\: + Inner\: radius$

$\implies \sf Outer\: radius =\: 0.2\: cm + 2\: cm$

$\implies \sf\bold{\green{Outer\: radius =\: 2.2\: cm}}$

So, their curved surface area will be :

$\implies \sf C.S.A =\: 2{\pi}r_2h$

$\implies \sf C.S.A =\: 2 \times \dfrac{22}{7} \times 2.2 \times 77$

$\implies \sf\bold{\blue{C.S.A =\: 1064.8\: {cm}^{2}}}$

Now, we have to find the area of the base :

As we know that :

$\longmapsto \sf\boxed{\bold{\pink{Area\: of\: base\: =\: {\pi}{r}^{2}_2 - {\pi}{r}^{2}_1}}}$

According to the question by using the formula we get,

$\implies \sf \dfrac{22}{7} \times {(2.2)}^{2} - \dfrac{22}{7} \times {(2)}^{2}$

$\implies \sf \dfrac{22}{7} \times \bigg[{(2.2)}^{2} - {(2)}^{2}\bigg]$

$\implies \sf \dfrac{22}{7} \times (4.84 - 4)$

$\implies \sf \dfrac{22}{7} \times 0.84$

$\implies \sf \dfrac{18.48}{7}$

$\implies \sf\bold{\purple{2.64\: {cm}^{2}}}$

Hence, the area of the base is 2.64 cm².

Now, we have to find the total surface area :

As we know that :

$\longmapsto \sf\boxed{\bold{\pink{T.S.A =\: C.S.A\: of\: inner\: cylinder\: + C.S.A\: of\: outer\: cylinder + 2 \times Area\: of\: base}}}$

Given :

• C.S.A of inner cylinder = 968 cm²
• C.S.A of outer cylinder = 1064.8 cm²
• Area of base = 2.64 cm²

According to the question by using the formula we get,

$\implies \sf T.S.A =\: 968 + 1064.8 + 2 \times 2.64$

$\implies \sf T.S.A =\: 2032.8 + 5.28$

$\implies \sf\bold{\red{T.S.A =\: 2038.08\: {cm}^{2}}}$

$\therefore$ The total surface area or TSA is 2038.08 cm².