Question

a metal pipe is 77cm long. the inner diameter of a cross section is 4cm , the outer diameter being 4.4cm finds its (¡) CSA (¡¡) TSA​

Answer 1

Given:-

• A metal pipe is 77 cm long. (length of pipe = 77 cm)
• The inner diameter of the pipe is 4 cm (d1 = 4 cm)
• The outer diameter of the pipe is 4.4 cm (d2 = 4.4 cm)

Find:-

• CSA (curved surface area)
• TSA (total surface area)

Solution:-

The inner diameter of the pipe is 4 cm.

So, the inner radius of pipe = 2 cm (half of the diameter)

The outer diameter of the pipe is 4.4 cm

So, the outer radius of pipe = 2.2 cm

$\sf{CSA\:of\:cylinder\:=\:2\pi\:rh}$

For outer radius

→ 2 × 22/7 × 2 × 77

→ 4 × 22 × 11

→ 968 cm²

For inner radius

→ 2 × 22/7 × 2.2 × 77

→ 4.4 × 22 × 11

→ 1064.8 cm²

Now,

$\sf{TSA\:of\:cylinder\:=\:Outer\:CSA\:+\:Inner\:CSA\:-\:thickness}$

→ 968 + 1064.8 - thickness ...(1)

Thickness = 2π (r2² - r1²)

→ 2 × 22/7 [(2.2)² - (2)²]

→ 44/7 (4.84 - 4)

→ 44/7 (0.84)

→ 5.28

Substitute value of thickness in (1)

→ 2032.8 + 5.28

→ 2038.08 cm²

•°• CSA for inner radius is 968 cm² and for outer radius is 1064.8 cm²

TSA of metal pipe is 2038.08 cm²

Answer 2

$\bold{\underline{\underline{\huge{\sf{AnsWer:}}}}}$

Inner Curved surface area is 968 sq.cm.

Outer curved surface area is 1064.8 sq.cm.

Total Surface area is 20.38.08 sq. cm

$\bold{\underline{\underline{\large{\sf{StEp\:by\:stEp\:explanation:}}}}}$

GiVeN :

• Cylinder :
• A metal pipe is 77cm long
• Inner diameter of a cross section is 4 cm
• The outer diameter is 4.4 cm

To FiNd :

• Curved surface area.
• Total surface area.

SoLuTiOn :

For inner diameter :

Diameter = 4 cm

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

$\implies$$\sf{inner\:radius\:=\:2\:cm}$

FoRmUlA fOr CuRvEd SuRfAcE :

$\bold{\large{\boxed{\red{\rm{CSA\:=\:2\:\pi\:r\:h}}}}}$

Where,

• r = inner radius = 2 cm
• h = height = 77 cm

Block in the values,

$\implies$$\sf{2\:\times\:{\dfrac{22}{7}\:\times\:2\:\times\:77}}$

$\implies$$\sf{\dfrac{44\:\times\:77\:\times\:2}{7}}$

$\implies$$\sf{\dfrac{88\:\times\:77}{7}}$

$\implies$$\sf{\dfrac{6776}{7}}$

$\implies$$\sf{968}$

$\sf{\therefore{Inner\:curved\:surface\:are\:=\:968\:cm^2}}$

FoR oUtEr DiAmEtEr :

Diameter = 4.4 cm

$\sf{\therefore{radius\:=\:{\dfrac{4.4}{2}}}}$

$\implies$$\sf{inner\:radius\:=\:2.2\:cm}$

Block in the values in the formula,

$\implies$$\sf{2\:\times\:{\dfrac{22}{7}\:\times\:2.2\:\times\:77}}$

$\implies$$\sf{\dfrac{44\:\times\:169.4}{7}}$

$\implies$$\sf{\dfrac{7453.6}{7}}$

$\implies$$\sf{1064.8}$

$\implies$$\sf{\therefore{Outer\:curved\:surface\:are\:=\:1064.8\:cm^2}}$

Now, before moving on to the total surface area, we need to first calculate the thickness of the pipe.

Ends of the pipe have circles with inner diameter of 4 cm (radius = 2 cm) and outer diameter of 4.4 cm (radius = 2.2 cm)

•°• Thickness of the edge of the pipe would be the difference of 2 times area of outer circle and the area of inner circle.

Thickness :

$\implies$$\sf{2\:\times(\pi\:r_1^2\:-\:\pi\:\:r_2^2)}$

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

$\implies$$\sf{2\:\times\:{\dfrac{22}{7}\:\times\:4.84\:-\:\times\:{\dfrac{22}{7}\:\times\:4}}}$

Taking $\sf{\dfrac{22}{7}}$ common.

$\implies$$\sf{\dfrac{44}{7}(4.84\:-\:4)}$

$\implies$$\sf{\dfrac{44}{7}\:\times\:0.84}$

$\implies$$\sf{\dfrac{36.96}{7}}$

$\implies$$\sf{5.28}$

•°• Thickness of the edge of the pipe is 5.28 cm

Now, total surface area will be the sum of inner curved surface area, outer curved surface area and the thickness.

Total surface area :

$\implies$$\sf{968\:+\:1064.8\:+\:5.28}$

$\implies$$\sf{2032.8\:+\:5.28}$

$\implies$$\sf{2038.08}$

•°• Inner Curved surface area is 968 sq.cm.

Outer curved surface area is 1064.8 sq. cm.

Total surface area is 2038.08 sq. cm