Question

3.
A metal pipe is 77 cm long. The inner diameter of a cross
section is 4 cm, the outer diameter being 4.4 cm
(see Fig. 13.11). Find its
(i) inner curved surface area.
(7) outer curved surface area
(ii) total surface area​

Answer 1

Answer:

here's your answer in the picture

Answer 2

Given :

• Length or height of metal pipe is 77cm.
• Inner Diameter = 4cm
• Outer Diameter = 4.4cm

To Find :

• Inner C.S.A.
• Outer C.S.A
• Total Surface Area.

Solution :

1. Inner Surface Area

$\longmapsto\tt{Height=77cm}$

$\longmapsto\tt{Radius(r)=\cancel\dfrac{4}{2}=2cm}$

Using Formula :

$\longmapsto\tt\boxed{C.S.A\:of\:Cylinder=2\pi{rh}}$

Putting Values :

$\longmapsto\tt{2\times\dfrac{22}{\cancel{7}}\times{2}\times{\cancel{77}}}$

$\longmapsto\tt{2\times{22}\times{2}\times{11}}$

$\longmapsto\tt\bold{968{cm}^{2}}$

_______________________

2.Outer Curved Surface Area

$\longmapsto\tt{Diameter=4.4cm}$

$\longmapsto\tt{Radius(R)=\cancel\dfrac{4.4}{2}=2.2cm}$

Using Formula :

$\longmapsto\tt\boxed{C.S.A\:of\:Cylinder=2\pi{rh}}$

Putting Values :

$\longmapsto\tt{2\times\dfrac{22}{\cancel{7}}\times\dfrac{22}{10}\times{\cancel{77}}}$

$\longmapsto\tt{\dfrac{10648}{10}}$

$\longmapsto\tt\bold{1064.8{cm}^{2}}$

_______________________

3.Total Surface Area

Inner S.A + Outer S.A + Area of 2 cylinderical bases.

$\longmapsto\tt{968+1064.8+2\pi{[{(R)}^{2}-{(r)}^{2}]}}$

$\longmapsto\tt{2032.8+2\times\dfrac{22}{7}[{(2.2)}^{2}-{(2)}^{2}]}$

$\longmapsto\tt{2032.8+2\times\dfrac{22}{7}(4.44-4)}$

$\longmapsto\tt{2032.8+2\times\dfrac{22}{7}(0.44)}$

$\longmapsto\tt\bold{2035.56{cm}^{2}(Approx.)}$