Math, asked by arjunpaudel337, 9 months ago

A metal pipe is 77 m long. The inner diameter of a cross section is 4 cm the outer diameter 4.4 cm. Find its
i) Inner curved area
ii) outer curved area
iii) Total surface area
iv) Volume of metal
Hint: Total surface area= Inner CSA + Outer CSA + 2* Area of base )
and area of base=22/7R Sq. - 22/7r Sq.

Answers

Answered by gk50839
4

Answer:

There is a inner Cylinder and Outer Cylinder. Inner Surface area of the Pipe = 2∏rh = 2*22*2*77/7 = 968 Square cm. Outer Surface area of the pipe = 2∏Rh = 2*22*2.2*77/7 = 1064.8 Square cm.

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Answered by SarcasticL0ve
1

Given:-

  • Length of metal pipe = 77 metre
  • The inner diameter of a cross section = 4 cm
  • The outer diameter of a cross section = 4.4cm

To find:-

  • i) Inner curved area
  • ii) outer curved area
  • iii) Total surface area
  • iv) Volume of metal

Solution:-

  • Inner radius (r) = \sf \dfrac{4}{2} = 2cm

  • Outer radius (R) = \sf \dfrac{4.4}{2} = 2.2cm

  • Height of Pipe (h) = 77 cm

\underline {\rule{261}{2}}

Inner surface area of the pipe:-

\dashrightarrow\sf 2 \pi rh \\ \\ \dashrightarrow\sf 2 \times \frac{22}{ \cancel{7}} \times 2 \times \cancel{77} \\ \\ \dashrightarrow\bf \red{968 cm^2}

\rule{200}3

Outer surface area of the pipe:-

\dashrightarrow\sf 2 \pi Rh \\ \\ \dashrightarrow\sf 2 \times \frac{22}{ \cancel{7}} \times 2.2 \times \cancel{77} \\ \\ \dashrightarrow\bf \red{1064.8 cm^2}

\rule{200}3

Total Surface Area:-

= Inner surface area + Outer surface area + 2( Area of cross section)

\dashrightarrow\sf 968 + 1064.8 + 2 \pi (R^2 - r^2) \\ \\ \dashrightarrow\sf 2032.8 + 2 \times \frac{22}{7} \bigg( (2.2)^2 - (2)^2 \bigg) \\ \\ \dashrightarrow\sf 2032.8 + 5.28 \\ \\ \dashrightarrow\bf \red{2038.08 cm^2}

\rule{200}3

Volume of metal:-

= Volume of outer pipe - Volume of inner pipe

\dashrightarrow\sf \pi R^2 h - \pi r^2 h \\ \\ \dashrightarrow\sf \pi h( R^2 - r^2) \\ \\ \dashrightarrow\sf \frac{22}{7} \times 77 \bigg( (2.2)^2 - (2)^2 \bigg) \\ \\ \dashrightarrow\sf \frac{22}{ \cancel{7}} \times \cancel{77} ( 4.84 - 4) \\ \\ \dashrightarrow\sf 154 \times 0.84 \\ \\ \dashrightarrow\bf \red{129.36 cm^3}

\underline {\rule{261}{2}}

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