Question

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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

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

Answer 2

external diameter of pipe given is 10cm

Step-by-step explanation:

radius=diameter/2

10/2=5

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

inner radius=9/2=4.5 cm

volume of metal pipe=outer volume-inner volume

πh(R²-r²)

• 22/7*35(5²-4.5²)=522.5 cm²=volume

mass=volume*density=7.8*522.5=4075.5 g

4.07kg