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The external diameter of a 35-cm-long metal pipe is 10 cm. If the pipe is 1 cm thick and the density of the metal is 7.8 g/cm^3, find the volume of the metal used in the pipe and the mass of the pipe.

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Answer 1

Question :

The external diameter of a 35-cm-long metal pipe is 10 cm. If the pipe is 1 cm thick and the density of the metal is 7.8 g/cm^3, find the volume of the metal used in the pipe and the mass of the pipe.

Answer :

Volume = 522.5cm³

Mass =4075.5g/4.075kg

Explanation:

The external diameter metal pipe = 10 cm

External radius of metal pipe = (R) diameter ÷ 2 = 10 ÷ 2 = 5cm

Inner diameter = outer diameter - thickness = 10 - 1 = 9 cm

Inner radius = (r) = 9cm ÷ 2 = 4.5cm

So, now

Volume of metal pipe = outer volume - inner volume

= πh[R² - r²]

= $= \frac{22}{7} \times 35$ [(5²) - (4.5)²]

= 22 × 5 [ 25 - 20.25]

= 110 × 4.75

= 522.5cm³

Now,

=Density of the metal = 7.8g/cm³

=Density = mass ÷ volume

=Mass = Density × volume

=7.8g/cm³ × 522.5cm³

= 4075.5g

• Hence the mass and the volume of the metal is 4075.5g/4.07kg and 522.5cm³ respectively