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/cm³ , find the volume of the metal used in the pipe and the mass of the pipe.​

Answer 1

Step-by-step explanation:

The external diameter of metal pipe=10cm

external radius of metal pipe=(R)diameter/2=10/2=5cm

the metal pipe is 35 cm long.

that is height of metal pipe=(h) =35 cm

thickness=1 cm

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

inner radius=(r)=9cm/2=4.5cm

volume of metal pipe=outer volume - inner volume

=πh[R²-r²]

=22/7×35[(5)²-(4.5)²]

=22×5[25-20.25]

=110×4.75=522.5cm³

density of a metal=7.8g/cm³

density=mass/volume

mass=density×volume=7.8g/cm³×522.5cm³=4075.5g

therefore volume of the metal is 522.5cm³ & mass of the pipe is 4075.5g/4.07 kg.

Answer 2

Given :-

Height = h = 35 cm

Thickness of pipe = 1 cm

Density of material = d = 7.8 g cm-³

External diameter of pipe = D = 10 cm

External radius of pipe = R = 5 cm

Internal radius = r = External radius - Thickness

r = 5 - 1 = 4 cm

First of all we are required to find out the volume of pipe.

Volume = V = Effective Area × Height

V = π(R² - r²) h

V = 22/7 × (5² - 4²) × 35

V = 22 × 5 × 9

$\bf{V\:=\:990\:{cm}^{3}}$

Now, We have to find out the Mass of material and we are given the density of material and from this we know a relation :-

Mass = Density × Volume

M = 7.8 × 990

M = 7722 g

M = 7.722 Kg

Hence,

Hence, The mass of material = M = 7.722 Kg✅

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