Question

A metal pipe has a bore (internal diameter) of 5 cm. The pipe is 2 mm thick all around. find the mass of 2 m long pipe if 1 cm³ of the metal has a
mass of 7.7 g.​

Answer 1

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Answer 2

QUESTION:-

A metal pipe has a bore (internal diameter) of 5 cm. The pipe is 2 mm thick all around. find the mass of 2 m long pipe if 1 cm³ of the metal has a

mass of 7.7 g.

ANSWER:-

LET →

•Internal radius of the metal pipe → r •External radius of the metal pipe → R •height → h

Then,

$r = \frac{5}{2} cm$

R ➠ r + thickness

$➠(\frac{5}{2} + \frac{2}{10} )cm$

$➠( \frac{5}{2} + \frac{1}{5} )cm$

$➠( \frac{25 + 2}{10} )cm$

$➠ \frac{27}{10} cm$

Volume of the metal =

➠ External volume - Internal volume

➠ πR²h - πr²h

➠ π( R² - r² ) h

$➠( \frac{22}{7} [( \frac{27}{10})^{2} - ( \frac{5}{2})^{2} ] \times 200){cm}^{3}$

$➠( \frac{22}{7} [( \frac{729}{100})- ( \frac{25}{4}) ] \times 200){cm}^{3}$

$➠( \frac{22}{7} [( \frac{729 - 625}{100}) ] \times 200){cm}^{3}$

$➠( \frac{22}{7} \times \frac{104}{100} \times 200){cm}^{3}$

$➠ \frac{4576}{7} {cm}^{3}$

Mass of 1 cm³ of the metal

➠ 7.7 g

Mass of 4576/7 cm³ of the metal

$➠ \frac{7.7 \times 4576}{7} g$

$➠ \frac{7.7 \times 4576}{7 \times 1000} kg$

➠ 5.0336 kg